What is the derivative of g(x)=ln((5x-2)^4) ?

The derivative of g(x)=ln((5x-2)^4) is (20)/(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 (20)/(5x-2)

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derivative of

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

\frac{20}{5 x - 2}

Solution steps

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

Apply the chain rule:

\frac{1}{( 5 x - 2 ) ^{4}} \frac{d}{d x} ((5 x - 2)^{4})

= \frac{1}{( 5 x - 2 ) ^{4}} \frac{d}{d x} ((5 x - 2)^{4})

\frac{d}{d x} ((5 x - 2)^{4}) = 20 (5 x - 2)^{3}

= \frac{1}{( 5 x - 2 ) ^{4}} \cdot 20 (5 x - 2)^{3}

Simplify

\frac{1}{( 5 x - 2 ) ^{4}} \cdot 20 (5 x - 2)^{3} : \frac{20}{5 x - 2}

= \frac{20}{5 x - 2}

\frac{4 d x}{d t} = 4 - 2 x

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