derivative of arctan^2(x^3)

解答

\frac{d}{d x} (arctan^{2} (x^{3}))

\frac{6 x ^{2} arctan ( x ^{3} )}{x ^{6} + 1}

求解步骤

\frac{d}{d x} (arctan^{2} (x^{3}))

使用连锁律:

2 arctan (x^{3}) \frac{d}{d x} (arctan (x^{3}))

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

\frac{d}{d x} (arctan (x^{3})) = \frac{3 x ^{2}}{x ^{6} + 1}

= 2 arctan (x^{3}) \frac{3 x ^{2}}{x ^{6} + 1}

化简

2 arctan (x^{3}) \frac{3 x ^{2}}{x ^{6} + 1} : \frac{6 x ^{2} arctan ( x ^{3} )}{x ^{6} + 1}

= \frac{6 x ^{2} arctan ( x ^{3} )}{x ^{6} + 1}

\frac{\partial}{\partial y} (e^{y} \cdot sin (x))

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

l a pl a ce t r an s f or m - 4 t^{2} δ (t - 2)

a re a 4 x^{2}, x^{2} + 3

y^{^{'}} = \frac{2 x}{y + x ^{2} y}