# How do you find the derivative of #y=3/4(x^(2)-1)^(2/3)#?

Steps:

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To find the derivative of ( y = \frac{3}{4}(x^2 - 1)^{2/3} ), you can use the chain rule.

First, differentiate the outer function with respect to the inner function:

( \frac{dy}{du} = \frac{2}{3}(x^2 - 1)^{-1/3} \cdot 2x )

Then, differentiate the inner function:

( \frac{du}{dx} = 2x )

Now, apply the chain rule:

( \frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx} = \frac{2}{3}(x^2 - 1)^{-1/3} \cdot 2x \cdot 2x )

Simplify:

( \frac{dy}{dx} = \frac{4x(x^2 - 1)^{-1/3}}{3} )

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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