derivative of sqrt(x)+1/(\sqrt[3]{x^4})

解答

\frac{d}{d x} (x + \frac{1}{3 x ^{4}})

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

求解步骤

\frac{d}{d x} (x + \frac{1}{3 x ^{4}})

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (\frac{1}{3 x ^{4}}) = - \frac{4}{3 x ^{\frac{7}{3}}}

= \frac{1}{2 x} - \frac{4}{3 x ^{\frac{7}{3}}}

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

\int \frac{1}{( x ^{2} ) ^{2}} d (x^{2})^{2}

\frac{d}{d x} (e^{2 x^{6}} - 1)

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

\frac{d}{d x} (\frac{10}{( 1 - x ) ^{3}})