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

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

We have:

Applying the power rule we have:

By signing up, you agree to our Terms of Service and Privacy Policy

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}} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7