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Popular Calculus >

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

Solution

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

Solution

\frac{6}{2 x + 5}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((2 x + 5)^{3}) = 6 (2 x + 5)^{2}

= \frac{1}{( 2 x + 5 ) ^{3}} \cdot 6 (2 x + 5)^{2}

Simplify

\frac{1}{( 2 x + 5 ) ^{3}} \cdot 6 (2 x + 5)^{2} : \frac{6}{2 x + 5}

= \frac{6}{2 x + 5}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln((2x+5^3)) ?
The derivative of ln((2x+5^3)) is 6/(2x+5)
What is the first derivative of ln((2x+5^3)) ?
The first derivative of ln((2x+5^3)) is 6/(2x+5)