What is the derivative of-4(8x^2+8)^{-6} ?

The derivative of-4(8x^2+8)^{-6} is (3x)/(16384(x^2+1)^7)

What is the first derivative of-4(8x^2+8)^{-6} ?

The first derivative of-4(8x^2+8)^{-6} is (3x)/(16384(x^2+1)^7)

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derivative of

- 4 (8 x^{2} + 8)^{- 6}

\frac{3 x}{16384 ( x ^{2} + 1 ) ^{7}}

Solution steps

\frac{d}{d x} (- 4 (8 x^{2} + 8)^{- 6})

Take the constant out:

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

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

Apply the chain rule:

- \frac{6}{( 8 x ^{2} + 8 ) ^{7}} \frac{d}{d x} (8 x^{2} + 8)

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

\frac{d}{d x} (8 x^{2} + 8) = 16 x

= - 4 (- \frac{6}{( 8 x ^{2} + 8 ) ^{7}} \cdot 16 x)

Simplify

- 4 (- \frac{6}{( 8 x ^{2} + 8 ) ^{7}} \cdot 16 x) : \frac{3 x}{16384 ( x ^{2} + 1 ) ^{7}}

= \frac{3 x}{16384 ( x ^{2} + 1 ) ^{7}}

(1 + x)^{^{'}}

f (x) = \frac{1}{7 ( 1 + x ^{2} )}, g (x) = \frac{1}{14} x^{2}

\int \frac{1 + 13 x}{x} d x

x \cdot y \cdot y^{^{'}} = y^{2} + 1

\int - 18 x^{2} d x

What is the derivative of-4(8x^2+8)^{-6} ?
The derivative of-4(8x^2+8)^{-6} is (3x)/(16384(x^2+1)^7)
What is the first derivative of-4(8x^2+8)^{-6} ?
The first derivative of-4(8x^2+8)^{-6} is (3x)/(16384(x^2+1)^7)