derivative of tan(e^{6x}+e^{tan(6x)})

解答

\frac{d}{d x} (tan (e^{6 x}) + e^{t a n (6 x)})

sec^{2} (e^{6 x}) e^{6 x} \cdot 6 + e^{t a n (6 x)} sec^{2} (6 x) \cdot 6

求解步骤

\frac{d}{d x} (tan (e^{6 x}) + e^{t a n (6 x)})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (tan (e^{6 x})) + \frac{d}{d x} (e^{t a n (6 x)})

\frac{d}{d x} (tan (e^{6 x})) = sec^{2} (e^{6 x}) e^{6 x} \cdot 6

\frac{d}{d x} (e^{t a n (6 x)}) = e^{t a n (6 x)} sec^{2} (6 x) \cdot 6

= sec^{2} (e^{6 x}) e^{6 x} \cdot 6 + e^{t a n (6 x)} sec^{2} (6 x) \cdot 6

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