What is the derivative of-7ln(5x^2-11) ?

The derivative of-7ln(5x^2-11) is -(70x)/(5x^2-11)

What is the first derivative of-7ln(5x^2-11) ?

The first derivative of-7ln(5x^2-11) is -(70x)/(5x^2-11)

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\frac{d}{d x} (- 7 ln (5 x^{2} - 11))

- \frac{70 x}{5 x ^{2} - 11}

Solution steps

\frac{d}{d x} (- 7 ln (5 x^{2} - 11))

Take the constant out:

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

= - 7 \frac{d}{d x} (ln (5 x^{2} - 11))

Apply the chain rule:

\frac{1}{5 x ^{2} - 11} \frac{d}{d x} (5 x^{2} - 11)

= \frac{1}{5 x ^{2} - 11} \frac{d}{d x} (5 x^{2} - 11)

\frac{d}{d x} (5 x^{2} - 11) = 10 x

= - 7 \cdot \frac{1}{5 x ^{2} - 11} \cdot 10 x

Simplify

- 7 \cdot \frac{1}{5 x ^{2} - 11} \cdot 10 x : - \frac{70 x}{5 x ^{2} - 11}

= - \frac{70 x}{5 x ^{2} - 11}

What is the derivative of-7ln(5x^2-11) ?
The derivative of-7ln(5x^2-11) is -(70x)/(5x^2-11)
What is the first derivative of-7ln(5x^2-11) ?
The first derivative of-7ln(5x^2-11) is -(70x)/(5x^2-11)