derivative of 5/(\sqrt[3]{x}-6/(2^x))

解答

\frac{d}{d x} (\frac{5}{3 x} - \frac{6}{2 ^{x}})

- \frac{5}{3 x ^{\frac{4}{3}}} + 3 ln (2) \cdot 2^{1 - x}

求解步骤

\frac{d}{d x} (\frac{5}{3 x} - \frac{6}{2 ^{x}})

化简

\frac{5}{3 x} - \frac{6}{2 ^{x}} : \frac{5}{3 x} - 3 \cdot 2^{1 - x}

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

使用微分加减法定则:

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

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

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

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

= - \frac{5}{3 x ^{\frac{4}{3}}} - (- 3 ln (2) \cdot 2^{1 - x})

化简

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

y^{^{'}} - \frac{3}{2} y = 3 t + 2 e^{t}

3 (y^{4} + 1) d x + (4 x y^{3}) d y = 0

\int \frac{1}{( y - 1 )} d y

x \to 4 lim (20 - x^{2})

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