# How do you find the derivative of #sqrt(x-3)#?

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

To find the derivative of (\sqrt{x-3}), you can use the chain rule. The chain rule states that if you have a composition of functions, (f(g(x))), then the derivative is (f'(g(x)) \cdot g'(x)).

So, let (f(u) = \sqrt{u}) and (g(x) = x - 3).

First, find (f'(u)) and (g'(x)): (f'(u) = \frac{1}{2\sqrt{u}}) and (g'(x) = 1).

Then, apply the chain rule: [\frac{d}{dx}(\sqrt{x-3}) = f'(g(x)) \cdot g'(x) = \frac{1}{2\sqrt{x-3}} \cdot 1 = \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.

- How do you differentiate implicitly #xy + y² - 2x = 0 # to find dy/dx and find the slope of the curve at the given point (1, -2)?
- How do you find the derivative of #y=(3x^2+5)(7x^3+8x) #?
- How do you differentiate #f(x)=(x+4)(cosx+2sinx)# using the product rule?
- What is the derivative of #f(x)= x^(4/5) (x-5)^2#?
- How do you implicitly differentiate #-y^2=e^(2x-4y)-2yx #?

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