derivative of cos^4(sin^3(x))

解答

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

- 12 cos^{3} (sin^{3} (x)) sin^{2} (x) sin (sin^{3} (x)) cos (x)

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (cos (sin^{3} (x))) = - sin (sin^{3} (x)) \cdot 3 sin^{2} (x) cos (x)

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

化简

= - 12 cos^{3} (sin^{3} (x)) sin^{2} (x) sin (sin^{3} (x)) cos (x)

d er i v a t i v e y = arccos (5 x)

\frac{d}{d x} (\frac{4}{x + 3})

\frac{d}{d x} (3 x - e^{x})

\frac{d y}{d x} - \frac{y}{x} = 1 - \frac{1}{x}

\frac{\partial}{\partial y} (tan (x y))