What is the derivative of f(x)=(3x^2-10)^{-14} ?

The derivative of f(x)=(3x^2-10)^{-14} is -(84x)/((3x^2-10)^{15)}

What is the first derivative of f(x)=(3x^2-10)^{-14} ?

The first derivative of f(x)=(3x^2-10)^{-14} is -(84x)/((3x^2-10)^{15)}

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derivative of

f (x) = (3 x^{2} - 10)^{- 14}

- \frac{84 x}{( 3 x ^{2} - 10 ) ^{15}}

Solution steps

\frac{d}{d x} ((3 x^{2} - 10)^{- 14})

Apply the chain rule:

- \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \frac{d}{d x} (3 x^{2} - 10)

= - \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \frac{d}{d x} (3 x^{2} - 10)

\frac{d}{d x} (3 x^{2} - 10) = 6 x

= - \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \cdot 6 x

Simplify

- \frac{14}{( 3 x ^{2} - 10 ) ^{15}} \cdot 6 x : - \frac{84 x}{( 3 x ^{2} - 10 ) ^{15}}

= - \frac{84 x}{( 3 x ^{2} - 10 ) ^{15}}

\frac{d}{d x} (\frac{3 x ^{2}}{5 x + 1})

f o u r i er t r an s f or m x

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What is the derivative of f(x)=(3x^2-10)^{-14} ?
The derivative of f(x)=(3x^2-10)^{-14} is -(84x)/((3x^2-10)^{15)}
What is the first derivative of f(x)=(3x^2-10)^{-14} ?
The first derivative of f(x)=(3x^2-10)^{-14} is -(84x)/((3x^2-10)^{15)}