derivative of 7^x+7cos((7x/2))

解

\frac{d}{d x} (7^{x} + 7 cos (\frac{7 x}{2}))

7^{x} ln (7) - \frac{49}{2} sin (\frac{7 x}{2})

解答ステップ

\frac{d}{d x} (7^{x} + 7 cos (\frac{7 x}{2}))

和/差の法則を適用:

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

= \frac{d}{d x} (7^{x}) + \frac{d}{d x} (7 cos (\frac{7 x}{2}))

\frac{d}{d x} (7^{x}) = 7^{x} ln (7)

\frac{d}{d x} (7 cos (\frac{7 x}{2})) = - \frac{49}{2} sin (\frac{7 x}{2})

= 7^{x} ln (7) - \frac{49}{2} sin (\frac{7 x}{2})