derivative of (1+sqrt(x)^3)

解答

\frac{d}{d x} ((1 + x)^{3})

\frac{3 ( 1 + x ) ^{2}}{2 x}

求解步骤

\frac{d}{d x} ((1 + x)^{3})

使用连锁律:

3 (1 + x)^{2} \frac{d}{d x} (1 + x)

= 3 (1 + x)^{2} \frac{d}{d x} (1 + x)

\frac{d}{d x} (1 + x) = \frac{1}{2 x}

= 3 (1 + x)^{2} \frac{1}{2 x}

化简

3 (1 + x)^{2} \frac{1}{2 x} : \frac{3 ( 1 + x ) ^{2}}{2 x}

= \frac{3 ( 1 + x ) ^{2}}{2 x}

\int_{1}^{3} \frac{x ^{2} + 7}{4 x - x ^{2}} d x

\frac{\partial}{\partial x} (2 x y e^{- x^{2} - y^{2}})

\frac{d}{d x} (6 sec (x) tan (x))

\int_{0}^{\infty} e^{\frac{x}{3}} d x

x^{2} \frac{d y}{d x} + 4 x y - y^{3} = 0