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Popular >

derivative of g(x)=[ln(5x-2)]^4

Solution

derivative of

g (x) = [ln (5 x - 2)]^{4}

Solution

\frac{20 ln ^{3} ( 5 x - 2 )}{5 x - 2}

Solution steps

\frac{d}{d x} ((ln (5 x - 2))^{4})

Apply the chain rule:

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

= 4 (ln (5 x - 2))^{3} \frac{d}{d x} (ln (5 x - 2))

\frac{d}{d x} (ln (5 x - 2)) = \frac{5}{5 x - 2}

= 4 (ln (5 x - 2))^{3} \frac{5}{5 x - 2}

Simplify

4 ln^{3} (5 x - 2) \frac{5}{5 x - 2} : \frac{20 ln ^{3} ( 5 x - 2 )}{5 x - 2}

= \frac{20 ln ^{3} ( 5 x - 2 )}{5 x - 2}

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Frequently Asked Questions (FAQ)

What is the derivative of g(x)=[ln(5x-2)]^4 ?
The derivative of g(x)=[ln(5x-2)]^4 is (20ln^3(5x-2))/(5x-2)
What is the first derivative of g(x)=[ln(5x-2)]^4 ?
The first derivative of g(x)=[ln(5x-2)]^4 is (20ln^3(5x-2))/(5x-2)