derivative cos^2(e^x+sqrt(x))

解

導関数

cos^{2} (e^{x} + x)

- sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

解答ステップ

\frac{d}{d x} (cos^{2} (e^{x} + x))

連鎖法則を適用:

2 cos (e^{x} + x) \frac{d}{d x} (cos (e^{x} + x))

= 2 cos (e^{x} + x) \frac{d}{d x} (cos (e^{x} + x))

\frac{d}{d x} (cos (e^{x} + x)) = - sin (e^{x} + x) (e^{x} + \frac{1}{2 x})

= 2 cos (e^{x} + x) (- sin (e^{x} + x) (e^{x} + \frac{1}{2 x}))

簡素化

2 cos (e^{x} + x) (- sin (e^{x} + x) (e^{x} + \frac{1}{2 x})) : - sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})

= - sin (2 (x + e^{x})) (\frac{1}{2 x} + e^{x})