What is the derivative of-5(7x^2+4)^{-6} ?

The derivative of-5(7x^2+4)^{-6} is (420x)/((7x^2+4)^7)

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

The first derivative of-5(7x^2+4)^{-6} is (420x)/((7x^2+4)^7)

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derivative of

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

\frac{420 x}{( 7 x ^{2} + 4 ) ^{7}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (7 x^{2} + 4) = 14 x

= - 5 (- \frac{6}{( 7 x ^{2} + 4 ) ^{7}} \cdot 14 x)

Simplify

- 5 (- \frac{6}{( 7 x ^{2} + 4 ) ^{7}} \cdot 14 x) : \frac{420 x}{( 7 x ^{2} + 4 ) ^{7}}

= \frac{420 x}{( 7 x ^{2} + 4 ) ^{7}}

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y = 8 x^{2} - 2 x, y = x^{3} - 8 x + 3

\frac{d y}{d x} = \frac{y ^{2} + x y + x ^{2}}{x ^{2}}

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What is the derivative of-5(7x^2+4)^{-6} ?
The derivative of-5(7x^2+4)^{-6} is (420x)/((7x^2+4)^7)
What is the first derivative of-5(7x^2+4)^{-6} ?
The first derivative of-5(7x^2+4)^{-6} is (420x)/((7x^2+4)^7)