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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

\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}

Simplify

\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}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln((5x^2+9^3)) ?
The derivative of ln((5x^2+9^3)) is (30x)/(5x^2+9)
What is the first derivative of ln((5x^2+9^3)) ?
The first derivative of ln((5x^2+9^3)) is (30x)/(5x^2+9)