What is the derivative of ln(5x^4) ?

The derivative of ln(5x^4) is 4/x

What is the first derivative of ln(5x^4) ?

The first derivative of ln(5x^4) is 4/x

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derivative of

ln (5 x^{4})

\frac{4}{x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{5 x ^{4}} \cdot 20 x^{3}

Simplify

\frac{1}{5 x ^{4}} \cdot 20 x^{3} : \frac{4}{x}

= \frac{4}{x}

What is the derivative of ln(5x^4) ?
The derivative of ln(5x^4) is 4/x
What is the first derivative of ln(5x^4) ?
The first derivative of ln(5x^4) is 4/x