What is the derivative of 4ln(9-5x^2) ?

The derivative of 4ln(9-5x^2) is -(40x)/(9-5x^2)

What is the first derivative of 4ln(9-5x^2) ?

The first derivative of 4ln(9-5x^2) is -(40x)/(9-5x^2)

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derivative of

4 ln (9 - 5 x^{2})

- \frac{40 x}{9 - 5 x ^{2}}

Solution steps

\frac{d}{d x} (4 ln (9 - 5 x^{2}))

Take the constant out:

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

= 4 \frac{d}{d x} (ln (9 - 5 x^{2}))

Apply the chain rule:

\frac{1}{9 - 5 x ^{2}} \frac{d}{d x} (9 - 5 x^{2})

= \frac{1}{9 - 5 x ^{2}} \frac{d}{d x} (9 - 5 x^{2})

\frac{d}{d x} (9 - 5 x^{2}) = - 10 x

= 4 \cdot \frac{1}{9 - 5 x ^{2}} (- 10 x)

Simplify

4 \cdot \frac{1}{9 - 5 x ^{2}} (- 10 x) : - \frac{40 x}{9 - 5 x ^{2}}

= - \frac{40 x}{9 - 5 x ^{2}}

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What is the derivative of 4ln(9-5x^2) ?
The derivative of 4ln(9-5x^2) is -(40x)/(9-5x^2)
What is the first derivative of 4ln(9-5x^2) ?
The first derivative of 4ln(9-5x^2) is -(40x)/(9-5x^2)