derivative \sqrt[3]{3+tan(t)}

解答

导数

3 3 + tan (t)

\frac{sec ^{2} ( t )}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}}

求解步骤

\frac{d}{d t} (3 3 + tan (t))

使用连锁律:

\frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} \frac{d}{d t} (3 + tan (t))

= \frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} \frac{d}{d t} (3 + tan (t))

\frac{d}{d t} (3 + tan (t)) = sec^{2} (t)

= \frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} sec^{2} (t)

化简

\frac{1}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}} sec^{2} (t) : \frac{sec ^{2} ( t )}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}}

= \frac{sec ^{2} ( t )}{3 ( 3 + tan ( t ) ) ^{\frac{2}{3}}}

y \frac{d y}{d x} + 8 x^{3} = 4

\frac{d}{d x} (\frac{42}{x})

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

t a y l or ln (x^{2} + 2)

y^{^{'}} = 1 + 2 x + y^{2} + 2 x y^{2}