What is the derivative of-ln(5x^2+7) ?

The derivative of-ln(5x^2+7) is -(10x)/(5x^2+7)

What is the first derivative of-ln(5x^2+7) ?

The first derivative of-ln(5x^2+7) is -(10x)/(5x^2+7)

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\frac{d}{d x} (- ln (5 x^{2} + 7))

- \frac{10 x}{5 x ^{2} + 7}

Solution steps

\frac{d}{d x} (- ln (5 x^{2} + 7))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (ln (5 x^{2} + 7))

Apply the chain rule:

\frac{1}{5 x ^{2} + 7} \frac{d}{d x} (5 x^{2} + 7)

= \frac{1}{5 x ^{2} + 7} \frac{d}{d x} (5 x^{2} + 7)

\frac{d}{d x} (5 x^{2} + 7) = 10 x

= - \frac{1}{5 x ^{2} + 7} \cdot 10 x

Simplify

- \frac{1}{5 x ^{2} + 7} \cdot 10 x : - \frac{10 x}{5 x ^{2} + 7}

= - \frac{10 x}{5 x ^{2} + 7}

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What is the derivative of-ln(5x^2+7) ?
The derivative of-ln(5x^2+7) is -(10x)/(5x^2+7)
What is the first derivative of-ln(5x^2+7) ?
The first derivative of-ln(5x^2+7) is -(10x)/(5x^2+7)