|
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
由， `d/dx x^n = n*x^(n-1)`.
又由， `链式法则：dy/dx = dy/(du)(du)/dx`.
那么， `d/dx (1 + sin(x))^3 = 3*(1 + sin(x))^(3 - 1)*d/dx (1 + sin(x))`.
我们知道， `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)`.
根据， `d/dx c = 0`.
所以， `d/dx 1 = 0`.
因为， `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))`
|