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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`. 所以, `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)`. 所以, `d/dx (1 + sin(x)) = d/dx 1 + d/dx sin(x)`. 我们知道, `d/dx c = 0`. 由此可得, `d/dx 1 = 0`. 根据, `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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