derivative sin^4(3x^2)

解答

导数

sin^{4} (3 x^{2})

24 x sin^{3} (3 x^{2}) cos (3 x^{2})

求解步骤

\frac{d}{d x} (sin^{4} (3 x^{2}))

使用连锁律:

4 (sin (3 x^{2}))^{3} \frac{d}{d x} (sin (3 x^{2}))

= 4 (sin (3 x^{2}))^{3} \frac{d}{d x} (sin (3 x^{2}))

\frac{d}{d x} (sin (3 x^{2})) = cos (3 x^{2}) \cdot 6 x

= 4 (sin (3 x^{2}))^{3} cos (3 x^{2}) \cdot 6 x

化简

= 24 x sin^{3} (3 x^{2}) cos (3 x^{2})

10 y^{^{'}} + 20 y = 12

2 (12) (18) + 2 (9) \frac{d y}{d t} = 0

\frac{d y}{d t} = 25 t^{4}

y^{^{'}} = \frac{6 x - 12}{x ^{2}}, y (1) = 20

\int 2 x ln (x^{2}) d x