derivative y=e^{arctan(3t^2)}

解答

导数

y = e^{a r c t a n (3 t^{2})}

\frac{6 e ^{a r c t a n (3 t^{2})} t}{9 t ^{4} + 1}

求解步骤

\frac{d}{d t} (e^{a r c t a n (3 t^{2})})

使用连锁律:

e^{a r c t a n (3 t^{2})} \frac{d}{d t} (arctan (3 t^{2}))

= e^{a r c t a n (3 t^{2})} \frac{d}{d t} (arctan (3 t^{2}))

\frac{d}{d t} (arctan (3 t^{2})) = \frac{6 t}{9 t ^{4} + 1}

= e^{a r c t a n (3 t^{2})} \frac{6 t}{9 t ^{4} + 1}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{6 e ^{a r c t a n (3 t^{2})} t}{9 t ^{4} + 1}

\frac{d}{d x} (5 x sin (π x))

\frac{d}{d x} (\frac{3000}{x + 3600 x ^{- 1}})

in v erse l a pl a ce \frac{9}{s ( s ^{2} + 2 s + 9 )}

t an g e n t f (x) = \frac{1}{x + 1}, (- 2, - 1)

\frac{d}{d x} ((6 x^{2} + 7 x)^{4})