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
我们知道, `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))`.
根据, `d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)`.
所以, `d/dx (1 + sin(x)) = d/dx 1 + d/dx sin(x)`.
因为, `d/dx c = 0`.
那么, `d/dx 1 = 0`.
我们知道, `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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