What is the derivative of ln(5x^2+1) ?

The derivative of ln(5x^2+1) is (10x)/(5x^2+1)

What is the first derivative of ln(5x^2+1) ?

The first derivative of ln(5x^2+1) is (10x)/(5x^2+1)

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

\frac{10 x}{5 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x^{2} + 1) = 10 x

= \frac{1}{5 x ^{2} + 1} \cdot 10 x

Simplify

\frac{1}{5 x ^{2} + 1} \cdot 10 x : \frac{10 x}{5 x ^{2} + 1}

= \frac{10 x}{5 x ^{2} + 1}

What is the derivative of ln(5x^2+1) ?
The derivative of ln(5x^2+1) is (10x)/(5x^2+1)
What is the first derivative of ln(5x^2+1) ?
The first derivative of ln(5x^2+1) is (10x)/(5x^2+1)