derivative f(x)=(2x-x^2)^3

解答

导数

f (x) = (2 x - x^{2})^{3}

3 (2 x - x^{2})^{2} (2 - 2 x)

求解步骤

\frac{d}{d x} ((2 x - x^{2})^{3})

使用连锁律:

3 (2 x - x^{2})^{2} \frac{d}{d x} (2 x - x^{2})

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

\frac{d}{d x} (2 x - x^{2}) = 2 - 2 x

= 3 (2 x - x^{2})^{2} (2 - 2 x)

y^{^{'}} = 3 - (2 y)

\frac{\partial}{\partial y} (ln (x^{2} + y^{3}))

s im pl i f y \frac{x - 5}{x}

\int_{4}^{9} \frac{1}{2} y^{\frac{1}{2}} + \frac{1}{2} y^{- \frac{1}{2}} d y

\frac{d}{d x} (a (2 e^{- 2 x} x - 2 e^{- 2 x} x^{2}))