derivative f(x)=tan^2(3e^x)

解

導関数

f (x) = tan^{2} (3 e^{x})

6 e^{x} sec^{2} (3 e^{x}) tan (3 e^{x})

解答ステップ

\frac{d}{d x} (tan^{2} (3 e^{x}))

連鎖法則を適用:

2 tan (3 e^{x}) \frac{d}{d x} (tan (3 e^{x}))

= 2 tan (3 e^{x}) \frac{d}{d x} (tan (3 e^{x}))

\frac{d}{d x} (tan (3 e^{x})) = sec^{2} (3 e^{x}) \cdot 3 e^{x}

= 2 tan (3 e^{x}) sec^{2} (3 e^{x}) \cdot 3 e^{x}

簡素化

= 6 e^{x} sec^{2} (3 e^{x}) tan (3 e^{x})