What is the derivative of ln(4x^5+1) ?

The derivative of ln(4x^5+1) is (20x^4)/(4x^5+1)

What is the first derivative of ln(4x^5+1) ?

The first derivative of ln(4x^5+1) is (20x^4)/(4x^5+1)

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derivative of

ln (4 x^{5} + 1)

\frac{20 x ^{4}}{4 x ^{5} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{5} + 1) = 20 x^{4}

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

Simplify

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

= \frac{20 x ^{4}}{4 x ^{5} + 1}

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What is the derivative of ln(4x^5+1) ?
The derivative of ln(4x^5+1) is (20x^4)/(4x^5+1)
What is the first derivative of ln(4x^5+1) ?
The first derivative of ln(4x^5+1) is (20x^4)/(4x^5+1)