derivative of 4e^x+2/(\sqrt[3]{x})

解答

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

4 e^{x} - \frac{2}{3 x ^{\frac{4}{3}}}

求解步骤

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

使用微分加减法定则:

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

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

\frac{d}{d x} (4 e^{x}) = 4 e^{x}

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

= 4 e^{x} - \frac{2}{3 x ^{\frac{4}{3}}}

s im pl i f y f (x) y

x \to 3 lim (\frac{( x ^{2} - 24 x + 25 ) ( x + 5 )}{x - 5})

x \to 7 + lim (\frac{x - 10}{x - 7})

\frac{d}{d x} (\frac{2 x}{- 8 x - 1})

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