derivative of ln((5x^2+9^3))

解答

\frac{d}{d x} (ln ((5 x^{2} + 9)^{3}))

\frac{30 x}{5 x ^{2} + 9}

求解步骤

\frac{d}{d x} (ln ((5 x^{2} + 9)^{3}))

使用连锁律:

\frac{1}{( 5 x ^{2} + 9 ) ^{3}} \frac{d}{d x} ((5 x^{2} + 9)^{3})

= \frac{1}{( 5 x ^{2} + 9 ) ^{3}} \frac{d}{d x} ((5 x^{2} + 9)^{3})

\frac{d}{d x} ((5 x^{2} + 9)^{3}) = 30 x (5 x^{2} + 9)^{2}

= \frac{1}{( 5 x ^{2} + 9 ) ^{3}} \cdot 30 x (5 x^{2} + 9)^{2}

化简

\frac{1}{( 5 x ^{2} + 9 ) ^{3}} \cdot 30 x (5 x^{2} + 9)^{2} : \frac{30 x}{5 x ^{2} + 9}

= \frac{30 x}{5 x ^{2} + 9}