# How do you find the derivative of # f(x) = 1/sqrt(x) #?

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

To find the derivative of ( f(x) = \frac{1}{\sqrt{x}} ), you can use the power rule for differentiation. The power rule states that if ( f(x) = x^n ), then ( f'(x) = nx^{n-1} ). Applying this rule to the given function:

( f(x) = x^{-\frac{1}{2}} )

Using the power rule:

( f'(x) = -\frac{1}{2}x^{-\frac{1}{2}-1} )

( f'(x) = -\frac{1}{2}x^{-\frac{3}{2}} )

Simplifying:

( f'(x) = -\frac{1}{2\sqrt{x^3}} )

So, the derivative of ( f(x) = \frac{1}{\sqrt{x}} ) is ( f'(x) = -\frac{1}{2\sqrt{x^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.

- What is the implicit derivative of #1= xe^y-sin(xy) #?
- What is the derivative of #(1-sinx)/cosx #?
- How do you differentiate #f(x)=(lnx+sinx)(xlnx-x)# using the product rule?
- How do you differentiate #f(x)=(x^2+sinx)(e^x-2x)# using the product rule?
- How do you differentiate #f(x)=(ln(x^2-3x)^-1)^(3/2)# using the chain rule?

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