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

The derivative of-7(6x^2+7)^{-6} is (504x)/((6x^2+7)^7)

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

The first derivative of-7(6x^2+7)^{-6} is (504x)/((6x^2+7)^7)

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derivative of

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

\frac{504 x}{( 6 x ^{2} + 7 ) ^{7}}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (6 x^{2} + 7) = 12 x

= - 7 (- \frac{6}{( 6 x ^{2} + 7 ) ^{7}} \cdot 12 x)

Simplify

- 7 (- \frac{6}{( 6 x ^{2} + 7 ) ^{7}} \cdot 12 x) : \frac{504 x}{( 6 x ^{2} + 7 ) ^{7}}

= \frac{504 x}{( 6 x ^{2} + 7 ) ^{7}}

\frac{c ^{4} - x ^{4}}{c ^{4} + x ^{4}}

\int sin (x^{3}) x^{2} d x

\int \frac{1 - x}{x ^{2}} d x

x \to 0 - lim (\frac{x - 1}{x ^{2}})

f (t) = sin (t^{2})

What is the derivative of-7(6x^2+7)^{-6} ?
The derivative of-7(6x^2+7)^{-6} is (504x)/((6x^2+7)^7)
What is the first derivative of-7(6x^2+7)^{-6} ?
The first derivative of-7(6x^2+7)^{-6} is (504x)/((6x^2+7)^7)