What is the derivative of-9(6x^2+7)^{-6} ?

The derivative of-9(6x^2+7)^{-6} is (648x)/((6x^2+7)^7)

What is the first derivative of-9(6x^2+7)^{-6} ?

The first derivative of-9(6x^2+7)^{-6} is (648x)/((6x^2+7)^7)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

- 9 (6 x^{2} + 7)^{- 6}

\frac{648 x}{( 6 x ^{2} + 7 ) ^{7}}

Solution steps

\frac{d}{d x} (- 9 (6 x^{2} + 7)^{- 6})

Take the constant out:

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

= - 9 \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

= - 9 (- \frac{6}{( 6 x ^{2} + 7 ) ^{7}} \cdot 12 x)

Simplify

- 9 (- \frac{6}{( 6 x ^{2} + 7 ) ^{7}} \cdot 12 x) : \frac{648 x}{( 6 x ^{2} + 7 ) ^{7}}

= \frac{648 x}{( 6 x ^{2} + 7 ) ^{7}}

(x^{2} + y^{2})^{2}

\frac{\partial}{\partial y} (3 z e^{x yz})

\frac{x ^{2}}{x + 8}

x^{^{'}} = e^{x}

\int 12 x^{2} d x

What is the derivative of-9(6x^2+7)^{-6} ?
The derivative of-9(6x^2+7)^{-6} is (648x)/((6x^2+7)^7)
What is the first derivative of-9(6x^2+7)^{-6} ?
The first derivative of-9(6x^2+7)^{-6} is (648x)/((6x^2+7)^7)