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

The derivative of y=-6(4x^2+4)^{-6} is (9x)/(512(x^2+1)^7)

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

The first derivative of y=-6(4x^2+4)^{-6} is (9x)/(512(x^2+1)^7)

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derivative of

y = - 6 (4 x^{2} + 4)^{- 6}

\frac{9 x}{512 ( x ^{2} + 1 ) ^{7}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{2} + 4) = 8 x

= - 6 (- \frac{6}{( 4 x ^{2} + 4 ) ^{7}} \cdot 8 x)

Simplify

- 6 (- \frac{6}{( 4 x ^{2} + 4 ) ^{7}} \cdot 8 x) : \frac{9 x}{512 ( x ^{2} + 1 ) ^{7}}

= \frac{9 x}{512 ( x ^{2} + 1 ) ^{7}}

What is the derivative of y=-6(4x^2+4)^{-6} ?
The derivative of y=-6(4x^2+4)^{-6} is (9x)/(512(x^2+1)^7)
What is the first derivative of y=-6(4x^2+4)^{-6} ?
The first derivative of y=-6(4x^2+4)^{-6} is (9x)/(512(x^2+1)^7)