在线求导

2023-12-24 02:36| 来源: 网络整理| 查看: 265

求导结果 / Derivative Result

`d/dx (1 + sin(x))^3 = 3*(1 + sin(x))^(3 - 1)*(0 + cos(x))`

解题步骤 / Steps to Solution

因为， `d/dx x^n = n*x^(n-1)`. 此外，由 `链式法则：dy/dx = dy/(du)(du)/dx`. 由此可得， `d/dx (1 + sin(x))^3 = 3*(1 + sin(x))^(3 - 1)*d/dx (1 + sin(x))`. 因为， `d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)`. 那么， `d/dx (1 + sin(x)) = d/dx 1 + d/dx sin(x)`. 因为， `d/dx c = 0`. 可得， `d/dx 1 = 0`. 由， `d/dx sin(x) = cos(x)`. 所以，根据定理：`d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)`, `d/dx (1 + sin(x)) = 0 + cos(x)` 所以，根据法则， `d/dx x^n = n*x^(n-1)`, 又因为, `链式法则：dy/dx = dy/(du)(du)/dx`, `d/dx (1 + sin(x))^3 = 3*(1 + sin(x))^(3 - 1)*(0 + cos(x))`

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