derivative of sin^3(5x^2)

解答

\frac{d}{d x} (sin^{3} (5 x^{2}))

30 x sin^{2} (5 x^{2}) cos (5 x^{2})

求解步骤

\frac{d}{d x} (sin^{3} (5 x^{2}))

使用连锁律:

3 (sin (5 x^{2}))^{2} \frac{d}{d x} (sin (5 x^{2}))

= 3 (sin (5 x^{2}))^{2} \frac{d}{d x} (sin (5 x^{2}))

\frac{d}{d x} (sin (5 x^{2})) = cos (5 x^{2}) \cdot 10 x

= 3 (sin (5 x^{2}))^{2} cos (5 x^{2}) \cdot 10 x

化简

= 30 x sin^{2} (5 x^{2}) cos (5 x^{2})

\int \frac{1}{5 x ^{3}} d x

t an g e n t f (x) = x^{4} - 20 x^{2} + 64, at x = - 2

f a c t or 24 x^{3} + 24 x^{2}

\frac{d}{d x} (2 x^{2} - \frac{1}{x ^{2}} + \frac{1}{x ^{3}})

\int \frac{31}{x ^{3} - 27} d x