derivative of 1/5 x^5+1/(12x^3)

解答

\frac{d}{d x} (\frac{1}{5} x^{5} + \frac{1}{12 x ^{3}})

x^{4} - \frac{1}{4 x ^{4}}

求解步骤

\frac{d}{d x} (\frac{1}{5} x^{5} + \frac{1}{12 x ^{3}})

化简

\frac{1}{5} x^{5} + \frac{1}{12 x ^{3}} : \frac{x ^{5}}{5} + \frac{1}{12 x ^{3}}

= \frac{d}{d x} (\frac{x ^{5}}{5} + \frac{1}{12 x ^{3}})

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{x ^{5}}{5}) + \frac{d}{d x} (\frac{1}{12 x ^{3}})

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

\frac{d}{d x} (\frac{1}{12 x ^{3}}) = - \frac{1}{4 x ^{4}}

= x^{4} - \frac{1}{4 x ^{4}}

x^{2} y^{^{'}} - 2 x y = sin (4 x) x^{4}

ma c l a u r in arctan (3 x)

\frac{d}{d t} (sin^{2} (t))

\frac{d}{d x} (6 e^{x} + 2 y)

(2 x - 4) \frac{d y}{d x} - y^{2} = 0