# How do you find the derivative of #f(x)=(8x^2-6)^-1#?

We use the chain rule here.

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To find the derivative of ( f(x) = (8x^2 - 6)^{-1} ), you can use the chain rule along with the power rule for differentiation. The chain rule states that if you have a composite function, you differentiate the outer function and then multiply by the derivative of the inner function.

First, let ( u = 8x^2 - 6 ). Then, differentiate ( u ) with respect to ( x ) to get ( \frac{du}{dx} ).

[ \frac{du}{dx} = 16x ]

Now, apply the chain rule:

[ \frac{df}{dx} = \frac{d}{dx} (u^{-1}) = -u^{-2} \cdot \frac{du}{dx} ]

Substitute ( u ) and ( \frac{du}{dx} ) back into the equation:

[ \frac{df}{dx} = -\frac{16x}{(8x^2 - 6)^2} ]

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