总述:本次共解1题。其中
☆整数计算1题
〖1/1整数列竖式计算〗
题型:整数乘法
原题:8248093374936943243527734573872009289119068940335579136*8248093374936943243527734573872009289119068940335579136Note that variables are case sensitive.\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {cos(x)}^{3}\ with\ respect\ to\ x:\\\end{split}\end{equation} \]
\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos^{3}(x)\\&\color{blue}{The\ first\ derivative\ function:}\\&\frac{d\left( cos^{3}(x)\right)}{dx}\\=&-3cos^{2}(x)sin(x)\\=&-3sin(x)cos^{2}(x)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -3sin(x)cos^{2}(x)\right)}{dx}\\=&-3cos(x)cos^{2}(x) - 3sin(x)*-2cos(x)sin(x)\\=&-3cos^{3}(x) + 6sin^{2}(x)cos(x)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( -3cos^{3}(x) + 6sin^{2}(x)cos(x)\right)}{dx}\\=&-3*-3cos^{2}(x)sin(x) + 6*2sin(x)cos(x)cos(x) + 6sin^{2}(x)*-sin(x)\\=&21sin(x)cos^{2}(x) - 6sin^{3}(x)\\\\ &\color{b恠
解:
8248093374936943243527734573872009289119068940335579136*8248093374936943243527734573872009289119068940335579136 = 68031044321678694594388214489561138418751116328668744577836642763015018725111538836125826312131885036518506496
列竖式计算:
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| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 1 | 6 | 4 | 9 | 6 | 1 | 8 | 6 | 7 | 4 | 9 | 8 | 7 | 3 | 8 | 8 | 6 | 4 | 8 | 7 | 0 | 5 | 5 | 4 | 6 | 9 | 1 | 4 | 7 | 7 | 4 | 4 | 0 | 1 | 8 | 5 | 7 | 8 | 2 | 3 | 8 | 1 | 3 | 7 | 8 | 8 | 0 | 6 | 7 | 1 | 1 | 5 | 8 | 2 | 7 | 2 | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 5 | 7 | 7 | 3 | 6 | 6 | 5 | 3 | 6 | 2 | 4 | 5 | 5 | 8 | 6 | 0 | 2 | 7 | 0 | 4 | 6 | 9 | 4 | 1 | 4 | 2 | 0 | 1 | 7 | 1 | 0 | 4 | 0 | 6 | 5 | 0 | 2 | 3 | 8 | 3 | 3 | 4 | 8 | 2 | 5 | 8 | 2 | 3 | 4 | 9 | 0 | 5 | 3 | 9 | 5 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 6 | 5 | 9 | 8 | 4 | 7 | 4 | 6 | 9 | 9 | 9 | 4 | 9 | 5 | 5 | 4 | 5 | 9 | 4 | 8 | 2 | 2 | 1 | 8 | 7 | 6 | 5 | 9 | 0 | 9 | 7 | 6 | 0 | 7 | 4 | 3 | 1 | 2 | 9 | 5 | 2 | 5 | 5 | 1 | 5 | 2 | 2 | 6 | 8 | 4 | 6 | 3 | 3 | 0 | 8 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 5 | 7 | 7 | 3 | 6 | 6 | 5 | 3 | 6 | 2 | 4 | 5 | 5 | 8 | 6 | 0 | 2 | 7 | 0 | 4 | 6 | 9 | 4 | 1 | 4 | 2 | 0 | 1 | 7 | 1 | 0 | 4 | 0 | 6 | 5 | 0 | 2 | 3 | 8 | 3 | 3 | 4 | 8 | 2 | 5 | 8 | 2 | 3 | 4 | 9 | 0 | 5 | 3 | 9 | 5 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 4 | 1 | 2 | 4 | 0 | 4 | 6 | 6 | 8 | 7 | 4 | 6 | 8 | 4 | 7 | 1 | 6 | 2 | 1 | 7 | 6 | 3 | 8 | 6 | 7 | 2 | 8 | 6 | 9 | 3 | 6 | 0 | 0 | 4 | 6 | 4 | 4 | 5 | 5 | 9 | 5 | 3 | 4 | 4 | 7 | 0 | 1 | 6 | 7 | 7 | 8 | 9 | 5 | 6 | 8 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 3 | 2 | 9 | 9 | 2 | 3 | 7 | 3 | 4 | 9 | 9 | 7 | 4 | 7 | 7 | 7 | 2 | 9 | 7 | 4 | 1 | 1 | 0 | 9 | 3 | 8 | 2 | 9 | 5 | 4 | 8 | 8 | 0 | 3 | 7 | 1 | 5 | 6 | 4 | 7 | 6 | 2 | 7 | 5 | 7 | 6 | 1 | 3 | 4 | 2 | 3 | 1 | 6 | 5 | 4 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | | 5 | 7 | 7 | 3 | 6 | 6 | 5 | 3 | 6 | 2 | 4 | 5 | 5 | 8 | 6 | 0 | 2 | 7 | 0 | 4 | 6 | 9 | 4 | 1 | 4 | 2 | 0 | 1 | 7 | 1 | 0 | 4 | 0 | 6 | 5 | 0 | 2 | 3 | 8 | 3 | 3 | 4 | 8 | 2 | 5 | 8 | 2 | 3 | 4 | 9 | 0 | 5 | 3 | 9 | 5 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | | 5 | 7 | 7 | 3 | 6 | 6 | 5 | 3 | 6 | 2 | 4 | 5 | 5 | 8 | 6 | 0 | 2 | 7 | 0 | 4 | 6 | 9 | 4 | 1 | 4 | 2 | 0 | 1 | 7 | 1 | 0 | 4 | 0 | 6 | 5 | 0 | 2 | 3 | 8 | 3 | 3 | 4 | 8 | 2 | 5 | 8 | 2 | 3 | 4 | 9 | 0 | 5 | 3 | 9 | 5 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | | 1 | 6 | 4 | 9 | 6 | 1 | 8 | 6 | 7 | 4 | 9 | 8 | 7 | 3 | 8 | 8 | 6 | 4 | 8 | 7 | 0 | 5 | 5 | 4 | 6 | 9 | 1 | 4 | 7 | 7 | 4 | 4 | 0 | 1 | 8 | 5 | 7 | 8 | 2 | 3 | 8 | 1 | 3 | 7 | 8 | 8 | 0 | 6 | 7 | 1 | 1 | 5 | 8 | 2 | 7 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | | 4 | 1 | 2 | 4 | 0 | 4 | 6 | 6 | 8 | 7 | 4 | 6 | 8 | 4 | 7 | 1 | 6 | 2 | 1 | 7 | 6 | 3 | 8 | 6 | 7 | 2 | 8 | 6 | 9 | 3 | 6 | 0 | 0 | 4 | 6 | 4 | 4 | 5 | 5 | 9 | 5 | 3 | 4 | 4 | 7 | 0 | 1 | 6 | 7 | 7 | 8 | 9 | 5 | 6 | 8 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | | 3 | 2 | 9 | 9 | 2 | 3 | 7 | 3 | 4 | 9 | 9 | 7 | 4 | 7 | 7 | 7 | 2 | 9 | 7 | 4 | 1 | 1 | 0 | 9 | 3 | 8 | 2 | 9 | 5 | 4 | 8 | 8 | 0 | 3 | 7 | 1 | 5 | 6 | 4 | 7 | 6 | 2 | 7 | 5 | 7 | 6 | 1 | 3 | 4 | 2 | 3 | 1 | 6 | 5 | 4 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | | 1 | 6 | 4 | 9 | 6 | 1 | 8 | 6 | 7 | 4 | 9 | 8 | 7 | 3 | 8 | 8 | 6 | 4 | 8 | 7 | 0 | 5 | 5 | 4 | 6 | 9 | 1 | 4 | 7 | 7 | 4 | 4 | 0 | 1 | 8 | 5 | 7 | 8 | 2 | 3 | 8 | 1 | 3 | 7 | 8 | 8 | 0 | 6 | 7 | 1 | 1 | 5 | 8 | 2 | 7 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | | 3 | 2 | 9 | 9 | 2 | 3 | 7 | 3 | 4 | 9 | 9 | 7 | 4 | 7 | 7 | 7 | 2 | 9 | 7 | 4 | 1 | 1 | 0 | 9 | 3 | 8 | 2 | 9 | 5 | 4 | 8 | 8 | 0 | 3 | 7 | 1 | 5 | 6 | 4 | 7 | 6 | 2 | 7 | 5 | 7 | 6 | 1 | 3 | 4 | 2 | 3 | 1 | 6 | 5 | 4 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | | 7 | 4 | 2 | 3 | 2 | 8 | 4 | 0 | 3 | 7 | 4 | 4 | 3 | 2 | 4 | 8 | 9 | 1 | 9 | 1 | 7 | 4 | 9 | 6 | 1 | 1 | 1 | 6 | 4 | 8 | 4 | 8 | 0 | 8 | 3 | 6 | 0 | 2 | 0 | 7 | 1 | 6 | 2 | 0 | 4 | 6 | 3 | 0 | 2 | 0 | 2 | 1 | 2 | 2 | 2 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | | 4 | 9 | 4 | 8 | 8 | 5 | 6 | 0 | 2 | 4 | 9 | 6 | 2 | 1 | 6 | 5 | 9 | 4 | 6 | 1 | 1 | 6 | 6 | 4 | 0 | 7 | 4 | 4 | 3 | 2 | 3 | 2 | 0 | 5 | 5 | 7 | 3 | 4 | 7 | 1 | 4 | 4 | 1 | 3 | 6 | 4 | 2 | 0 | 1 | 3 | 4 | 7 | 4 | 8 | 1 | 6 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | | 7 | 4 | 2 | 3 | 2 | 8 | 4 | 0 | 3 | 7 | 4 | 4 | 3 | 2 | 4 | 8 | 9 | 1 | 9 | 1 | 7 | 4 | 9 | 6 | 1 | 1 | 1 | 6 | 4 | 8 | 4 | 8 | 0 | 8 | 3 | 6 | 0 | 2 | 0 | 7 | 1 | 6 | 2 | 0 | 4 | 6 | 3 | 0 | 2 | 0 | 2 | 1 | 2 | 2 | 2 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | | 3 | 2 | 9 | 9 | 2 | 3 | 7 | 3 | 4 | 9 | 9 | 7 | 4 | 7 | 7 | 7 | 2 | 9 | 7 | 4 | 1 | 1 | 0 | 9 | 3 | 8 | 2 | 9 | 5 | 4 | 8 | 8 | 0 | 3 | 7 | 1 | 5 | 6 | 4 | 7 | 6 | 2 | 7 | 5 | 7 | 6 | 1 | 3 | 4 | 2 | 3 | 1 | 6 | 5 | 4 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | | 5 | 7 | 7 | 3 | 6 | 6 | 5 | 3 | 6 | 2 | 4 | 5 | 5 | 8 | 6 | 0 | 2 | 7 | 0 | 4 | 6 | 9 | 4 | 1 | 4 | 2 | 0 | 1 | 7 | 1 | 0 | 4 | 0 | 6 | 5 | 0 | 2 | 3 | 8 | 3 | 3 | 4 | 8 | 2 | 5 | 8 | 2 | 3 | 4 | 9 | 0 | 5 | 3 | 9 | 5 | 2 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | | 2 | 4 | 7 | 4 | 4 | 2 | 8 | 0 | 1 | 2 | 4 | 8 | 1 | 0 | 8 | 2 | 9 | 7 | 3 | 0 | 5 | 8 | 3 | 2 | 0 | 3 | 7 | 2 | 1 | 6 | 1 | 6 | 0 | 2 | 7 | 8 | 6 | 7 | 3 | 5 | 7 | 2 | 0 | 6 | 8 | 2 | 1 | 0 | 0 | 6 | 7 | 3 | 7 | 4 | 0 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 7 | 4 | 2 | 3 | 2 | 8 | 4 | 0 | 3 | 7 | 4 | 4 | 3 | 2 | 4 | 8 | 9 | 1 | 9 | 1 | 7 | 4 | 9 | 6 | 1 | 1 | 1 | 6 | 4 | 8 | 4 | 8 | 0 | 8 | 3 | 6 | 0 | 2 | 0 | 7 | 1 | 6 | 2 | 0 | 4 | 6 | 3 | 0 | 2 | 0 | 2 | 1 | 2 | 2 | 2 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | | 6 | 5 | 9 | 8 | 4 | 7 | 4 | 6 | 9 | 9 | 9 | 4 | 9 | 5 | 5 | 4 | 5 | 9 | 4 | 8 | 2 | 2 | 1 | 8 | 7 | 6 | 5 | 9 | 0 | 9 | 7 | 6 | 0 | 7 | 4 | 3 | 1 | 2 | 9 | 5 | 2 | 5 | 5 | 1 | 5 | 2 | 2 | 6 | 8 | 4 | 6 | 3 | 3 | 0 | 8 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| | | | | | | | 3 | 2 | 9 | 9 | 2 | 3 | 7 | 3 | 4 | 9 | 9 | 7 | 4 | 7 | 7 | 7 | 2 | 9 | 7 | 4 | 1 | 1 | 0 | 9 | 3 | 8 | 2 | 9 | 5 | 4 | 8 | 8 | 0 | 3 | 7 | 1 | 5 | 6 | 4 | 7 | 6 | 2 | 7 | 5 | 7 | 6 | 1 | 3 | 4 | 2 | 3 | 1 | 6 | 5 | 4 | 4 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
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| | | | | | 6 | 5 | 9 | 8 | 4 | 7 | 4 | 6 | 9 | 9 | 9 | 4 | 9 | 5 | 5 | 4 | 5 | 9 | 4 | 8 | 2 | 2 | 1 | 8 | 7 | 6 | 5 | 9 | 0 | 9 | 7 | 6 | 0 | 7 | 4 | 3 | 1 | 2 | 9 | 5 | 2 | 5 | 5 | 1 | 5 | 2 | 2 | 6 | 8 | 4 | 6 | 3 | 3 | 0 | 8 | 8 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
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| | | | | | 6 | 8 | 0 | 3 | 1 | 0 | 4 | 4 | 3 | 2 | 1 | 6 | 7 | 8 | 6 | 9 | 4 | 5 | 9 | 4 | 3 | 8 | 8 | 2 | 1 | 4 | 4 | 8 | 9 | 5 | 6 | 1 | 1 | 3 | 8 | 4 | 1 | 8 | 7 | 5 | 1 | 1 | 1 | 6 | 3 | 2 | 8 | 6 | 6 | 8 | 7 | 4 | 4 | 5 | 7 | 7 | 8 | 3 | 6 | 6 | 4 | 2 | 7 | 6 | 3 | 0 | 1 | 5 | 0 | 1 | 8 | 7 | 2 | 5 | 1 | 1 | 1 | 5 | 3 | 8 | 8 | 3 | 6 | 1 | 2 | 5 | 8 | 2 | 6 | 3 | 1 | 2 | 1 | 3 | 1 | 8 | 8 | 5 | 0 | 3 | 6 | 5 | 1 | 8 | 5 | 0 | 6 | 4 | 9 | 6 |
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