derivative cos^3(e^{4x})

解答

导数

cos^{3} (e^{4 x})

- 12 e^{4 x} cos^{2} (e^{4 x}) sin (e^{4 x})

求解步骤

\frac{d}{d x} (cos^{3} (e^{4 x}))

使用连锁律:

3 (cos (e^{4 x}))^{2} \frac{d}{d x} (cos (e^{4 x}))

= 3 (cos (e^{4 x}))^{2} \frac{d}{d x} (cos (e^{4 x}))

\frac{d}{d x} (cos (e^{4 x})) = - sin (e^{4 x}) e^{4 x} \cdot 4

= 3 (cos (e^{4 x}))^{2} (- sin (e^{4 x}) e^{4 x} \cdot 4)

化简

= - 12 e^{4 x} cos^{2} (e^{4 x}) sin (e^{4 x})