# How do you use the power rule to differentiate #f(x)=3x^5+2/sqrtx#?

We can rewrite the equation so we can apply the power rule.

Then when we differentiate using the power rule:

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To differentiate ( f(x) = \frac{3x^5 + 2}{\sqrt{x}} ) using the power rule, follow these steps:

- Rewrite the function as ( f(x) = 3x^5 \cdot x^{-\frac{1}{2}} + 2x^{-\frac{1}{2}} ).
- Apply the power rule to each term individually.
- For the first term, ( 3x^5 \cdot x^{-\frac{1}{2}} ), apply the power rule to get ( 15x^{5-1} ).
- For the second term, ( 2x^{-\frac{1}{2}} ), apply the power rule to get ( -x^{-\frac{1}{2}-1} ).
- Simplify the results to obtain the final derivative.

The derivative of ( f(x) = \frac{3x^5 + 2}{\sqrt{x}} ) using the power rule is:

[ f'(x) = 15x^4 - \frac{1}{2}x^{-\frac{3}{2}} ]

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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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