What is the derivative of (3x^2-9^{-14}) ?

The derivative of (3x^2-9^{-14}) is -(28x)/(4782969(x^2-3)^{15)}

What is the first derivative of (3x^2-9^{-14}) ?

The first derivative of (3x^2-9^{-14}) is -(28x)/(4782969(x^2-3)^{15)}

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\frac{d}{d x} ((3 x^{2} - 9)^{- 14})

- \frac{28 x}{4782969 ( x ^{2} - 3 ) ^{15}}

Solution steps

\frac{d}{d x} ((3 x^{2} - 9)^{- 14})

Apply the chain rule:

- \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \frac{d}{d x} (3 x^{2} - 9)

= - \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \frac{d}{d x} (3 x^{2} - 9)

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

= - \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \cdot 6 x

Simplify

- \frac{14}{( 3 x ^{2} - 9 ) ^{15}} \cdot 6 x : - \frac{28 x}{4782969 ( x ^{2} - 3 ) ^{15}}

= - \frac{28 x}{4782969 ( x ^{2} - 3 ) ^{15}}

What is the derivative of (3x^2-9^{-14}) ?
The derivative of (3x^2-9^{-14}) is -(28x)/(4782969(x^2-3)^{15)}
What is the first derivative of (3x^2-9^{-14}) ?
The first derivative of (3x^2-9^{-14}) is -(28x)/(4782969(x^2-3)^{15)}