derivative of sqrt(x^3+x^5)

解答

\frac{d}{d x} (x^{3} + x^{5})

\frac{3 x ^{2} + 5 x ^{4}}{2 x ^{3} + x ^{5}}

求解步骤

\frac{d}{d x} (x^{3} + x^{5})

使用连锁律:

\frac{1}{2 x ^{3} + x ^{5}} \frac{d}{d x} (x^{3} + x^{5})

= \frac{1}{2 x ^{3} + x ^{5}} \frac{d}{d x} (x^{3} + x^{5})

\frac{d}{d x} (x^{3} + x^{5}) = 3 x^{2} + 5 x^{4}

= \frac{1}{2 x ^{3} + x ^{5}} (3 x^{2} + 5 x^{4})

化简

\frac{1}{2 x ^{3} + x ^{5}} (3 x^{2} + 5 x^{4}) : \frac{3 x ^{2} + 5 x ^{4}}{2 x ^{3} + x ^{5}}

= \frac{3 x ^{2} + 5 x ^{4}}{2 x ^{3} + x ^{5}}

\int \frac{x}{2 - x ^{2}} d x

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

(\frac{f ( t )}{g ( t )})^{'}

\frac{d}{d x} (x e^{x^{2}} (x^{2} + 1)^{10})

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