What is the derivative of-9(5x^2+4)^{-6} ?

The derivative of-9(5x^2+4)^{-6} is (540x)/((5x^2+4)^7)

What is the first derivative of-9(5x^2+4)^{-6} ?

The first derivative of-9(5x^2+4)^{-6} is (540x)/((5x^2+4)^7)

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derivative of

- 9 (5 x^{2} + 4)^{- 6}

\frac{540 x}{( 5 x ^{2} + 4 ) ^{7}}

Solution steps

\frac{d}{d x} (- 9 (5 x^{2} + 4)^{- 6})

Take the constant out:

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

= - 9 \frac{d}{d x} ((5 x^{2} + 4)^{- 6})

Apply the chain rule:

- \frac{6}{( 5 x ^{2} + 4 ) ^{7}} \frac{d}{d x} (5 x^{2} + 4)

= - \frac{6}{( 5 x ^{2} + 4 ) ^{7}} \frac{d}{d x} (5 x^{2} + 4)

\frac{d}{d x} (5 x^{2} + 4) = 10 x

= - 9 (- \frac{6}{( 5 x ^{2} + 4 ) ^{7}} \cdot 10 x)

Simplify

- 9 (- \frac{6}{( 5 x ^{2} + 4 ) ^{7}} \cdot 10 x) : \frac{540 x}{( 5 x ^{2} + 4 ) ^{7}}

= \frac{540 x}{( 5 x ^{2} + 4 ) ^{7}}

What is the derivative of-9(5x^2+4)^{-6} ?
The derivative of-9(5x^2+4)^{-6} is (540x)/((5x^2+4)^7)
What is the first derivative of-9(5x^2+4)^{-6} ?
The first derivative of-9(5x^2+4)^{-6} is (540x)/((5x^2+4)^7)