How do you use the chain rule to differentiate #y=4(x^2-7x+3)^(-3/4)#?
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To differentiate ( y = 4(x^2 - 7x + 3)^{-3/4} ) using the chain rule, follow these steps:
- Identify the inner function ( u = x^2 - 7x + 3 ).
- Compute its derivative ( \frac{du}{dx} ).
- Apply the power rule to ( u ), resulting in ( \frac{d}{du} [u^{-3/4}] ).
- Apply the chain rule by multiplying ( \frac{d}{du} [u^{-3/4}] ) by ( \frac{du}{dx} ).
- Simplify the expression to get the final result.
The derivative of ( y ) with respect to ( x ) is:
[ \frac{dy}{dx} = 4 \cdot \left(-\frac{3}{4}\right) \cdot (x^2 - 7x + 3)^{-7/4} \cdot (2x - 7) ]
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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.
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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