derivative y=-4/(5x^5)+(15)/(4x^4)

解答

导数

y = - \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}}

\frac{4}{x ^{6}} - \frac{15}{x ^{5}}

求解步骤

\frac{d}{d x} (- \frac{4}{5 x ^{5}} + \frac{15}{4 x ^{4}})

使用微分加减法定则:

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

= - \frac{d}{d x} (\frac{4}{5 x ^{5}}) + \frac{d}{d x} (\frac{15}{4 x ^{4}})

\frac{d}{d x} (\frac{4}{5 x ^{5}}) = - \frac{4}{x ^{6}}

\frac{d}{d x} (\frac{15}{4 x ^{4}}) = - \frac{15}{x ^{5}}

= - (- \frac{4}{x ^{6}}) - \frac{15}{x ^{5}}

化简

= \frac{4}{x ^{6}} - \frac{15}{x ^{5}}

d er i v a t i v e f (x) = x^{2} + 21

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

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

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

x \to 0 lim (\frac{sin ( 4 x )}{( 2 x )})