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Popular Calculus >

derivative of (3x^2-9^{-12})

Solution

\frac{d}{d x} ((3 x^{2} - 9)^{- 12})

Solution

- \frac{8 x}{177147 ( x ^{2} - 3 ) ^{13}}

Solution steps

\frac{d}{d x} ((3 x^{2} - 9)^{- 12})

Apply the chain rule:

- \frac{12}{( 3 x ^{2} - 9 ) ^{13}} \frac{d}{d x} (3 x^{2} - 9)

= - \frac{12}{( 3 x ^{2} - 9 ) ^{13}} \frac{d}{d x} (3 x^{2} - 9)

\frac{d}{d x} (3 x^{2} - 9) = 6 x

= - \frac{12}{( 3 x ^{2} - 9 ) ^{13}} \cdot 6 x

Simplify

- \frac{12}{( 3 x ^{2} - 9 ) ^{13}} \cdot 6 x : - \frac{8 x}{177147 ( x ^{2} - 3 ) ^{13}}

= - \frac{8 x}{177147 ( x ^{2} - 3 ) ^{13}}

Graph

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area y= 4/3 ,y= 1/(sqrt(9-x^2))

a re a y = \frac{4}{3}, y = \frac{1}{9 - x ^{2}}

integral from-1 to 1/2 of 1/4 (3x^2+1)

\int_{- 1}^{\frac{1}{2}} \frac{1}{4} (3 x^{2} + 1) d x

y^{^{'}} = 1 - x + 4 y

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2-9^{-12}) ?
The derivative of (3x^2-9^{-12}) is -(8x)/(177147(x^2-3)^{13)}
What is the first derivative of (3x^2-9^{-12}) ?
The first derivative of (3x^2-9^{-12}) is -(8x)/(177147(x^2-3)^{13)}