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

Answer 1

#f'(x)=15x^4-1/x^(3/2)#

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

#f(x)=3x^5+2x^(-1/2)#

Then when we differentiate using the power rule:

#f'(x) = d/dx(3x^5)+d/dx(2x^(-1/2))#
#f'(x) = (3)(5)(x^(5-1))+(2)(-1/2)(x^(-1/2-1))#
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Answer 2

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

  1. Rewrite the function as ( f(x) = 3x^5 \cdot x^{-\frac{1}{2}} + 2x^{-\frac{1}{2}} ).
  2. Apply the power rule to each term individually.
  3. For the first term, ( 3x^5 \cdot x^{-\frac{1}{2}} ), apply the power rule to get ( 15x^{5-1} ).
  4. For the second term, ( 2x^{-\frac{1}{2}} ), apply the power rule to get ( -x^{-\frac{1}{2}-1} ).
  5. 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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Answer from HIX Tutor

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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