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求导结果 / Derivative Result `d/dx 10*(x + tan(x)) = 10*(1 + (sec(x))^2)`解题步骤 / Steps to Solution 根据, `d/dx cf(x) = c d/dx f(x)`. 可得, `d/dx 10*(x + tan(x)) = 10*d/dx (x + tan(x))`. 因为, `d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)`. 可得, `d/dx (x + tan(x)) = d/dx x + d/dx tan(x)`. 由, `d/dx x = 1`. 我们知道, `d/dx tan(x) = sec^2(x)`. 所以,根据定理:`d/dx (f(x) + g(x)) = d/dx f(x) + d/dx g(x)`, `d/dx (x + tan(x)) = 1 + (sec(x))^2` 所以,根据定理:`d/dx cf(x) = c d/dx f(x)`, `d/dx 10*(x + tan(x)) = 10*(1 + (sec(x))^2)` |
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