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How do you find the derivative of #f(x)=(8x+3)^.5#?

Answer 1

Paisley Johnson

# f'(x) = 4/sqrt(8x+3)#

We have:

# f(x) = (8x+3)^.5 ( = sqrt(8x+3))#

Applying the power rule we have:

# f'(x) = 1/2(8x+3)^(-1/2)(8)# # " " = 4(8x+3)^(-1/2)# # " " = 4/sqrt(8x+3)#

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Answer 2

William Abdalla

To find the derivative of ( f(x) = (8x + 3)^{0.5} ), you can use the chain rule. The chain rule states that if you have a function within another function, you take the derivative of the outer function and multiply it by the derivative of the inner function.

First, differentiate the outer function ( u = \sqrt{x} ) with respect to ( x ), which is ( \frac{1}{2}(8x + 3)^{-0.5} ). Then, differentiate the inner function ( v = 8x + 3 ) with respect to ( x ), which is ( 8 ).

Applying the chain rule, the derivative of ( f(x) ) with respect to ( x ) is ( \frac{1}{2}(8x + 3)^{-0.5} \times 8 ). Simplifying this expression gives ( \frac{4}{\sqrt{8x + 3}} ).

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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.