# How do you find the derivative of #f(x)=x^-100#?

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

To find the derivative of ( f(x) = x^{-100} ), 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 ( f(x) = x^{-100} ), we have:

[ f'(x) = -100x^{-100-1} ]

Simplify the exponent:

[ f'(x) = -100x^{-101} ]

So, the derivative of ( f(x) = x^{-100} ) is ( f'(x) = -100x^{-101} ).

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.

- How do you differentiate #g(t)=1/(t^4+1)^3#?
- How do you integrate #f(x)=(2-2x+2x^2-2x^3-3x^4)(1+x-2x^2-3x^3)# using the product rule?
- How do you use the chain rule to differentiate #y = e^lnx#?
- If #f(x) =-sqrt(3x-1) # and #g(x) = (x+3)^3 #, what is #f'(g(x)) #?
- How do you differentiate #r=5theta^2sectheta#?

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