# How do you differentiate # f(x)=(2x+1)^(5/2) (4x-1)^(3/4) # using the product rule?

See pointer for calculation method in Explanation

Substitute into:

Once that is done it is a matter of simplification!

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To differentiate ( f(x) = (2x + 1)^{5/2} \cdot (4x - 1)^{3/4} ) using the product rule, follow these steps:

- Identify the two functions being multiplied: ( u = (2x + 1)^{5/2} ) and ( v = (4x - 1)^{3/4} ).
- Calculate the derivatives of each function: ( u' = \frac{5}{2}(2x + 1)^{3/2} \cdot 2 ) and ( v' = \frac{3}{4}(4x - 1)^{-1/4} \cdot 4 ).
- Apply the product rule: ( f'(x) = u'v + uv' ).

After substituting the derivatives and the original functions into the product rule formula, simplify the expression to obtain the derivative of ( f(x) ).

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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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