derivative of ln(sin^3(x^2+7))

解答

\frac{d}{d x} (ln (sin^{3} (x^{2} + 7)))

6 x cot (x^{2} + 7)

求解步骤

\frac{d}{d x} (ln (sin^{3} (x^{2} + 7)))

使用连锁律:

\frac{1}{sin ^{3} ( x ^{2} + 7 )} \frac{d}{d x} (sin^{3} (x^{2} + 7))

= \frac{1}{sin ^{3} ( x ^{2} + 7 )} \frac{d}{d x} (sin^{3} (x^{2} + 7))

\frac{d}{d x} (sin^{3} (x^{2} + 7)) = 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7)

= \frac{1}{sin ^{3} ( x ^{2} + 7 )} \cdot 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7)

化简

\frac{1}{sin ^{3} ( x ^{2} + 7 )} \cdot 6 x sin^{2} (x^{2} + 7) cos (x^{2} + 7) : 6 x cot (x^{2} + 7)

= 6 x cot (x^{2} + 7)

t an g e n t y^{3} + x y^{2} - 61 = x + 3 y^{2}, at x = 3

\int \frac{x ^{2}}{2 - x} d x

\int cot (10 x) csc^{4} (10 z)

\int x^{3} - 4 x^{- 2} + 5 d x

\int_{0}^{2} 3 d x