derivative sin^4(3x-4x^2)

解答

导数

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

4 sin^{3} (3 x - 4 x^{2}) cos (3 x - 4 x^{2}) (3 - 8 x)

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (sin (3 x - 4 x^{2})) = cos (3 x - 4 x^{2}) (3 - 8 x)

= 4 (sin (3 x - 4 x^{2}))^{3} cos (3 x - 4 x^{2}) (3 - 8 x)

化简

= 4 sin^{3} (3 x - 4 x^{2}) cos (3 x - 4 x^{2}) (3 - 8 x)

d er i v a t i v e - (e^{- x})^{2}

d er i v a t i v e lo g_{10} (x - 1)

\frac{d}{d s} (3 s^{2})

d er i v a t i v e y = \frac{( x ^{5} + x ^{2} )}{( x ^{3} + 1 )}

\frac{d}{d t} (65 + 2 t - 3 t^{2})