derivative of 2^{x^3-2}-1/(x^2)

解答

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

3 ln (2) \cdot 2^{x^{3} - 2} x^{2} + \frac{2}{x ^{3}}

求解步骤

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

使用微分加减法定则:

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

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

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

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

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

化简

= 3 ln (2) \cdot 2^{x^{3} - 2} x^{2} + \frac{2}{x ^{3}}

\frac{\partial}{\partial x} (\frac{6}{x ^{3}})

\frac{d}{d x} (\frac{20}{x ^{3}})

\int 3 x^{2} - 5 x + 2 d x

\int_{0}^{\infty} 6 e^{- 3 x} d x

\frac{d}{d x} (\frac{x - 19}{x - 19})