# Using the limit definition, how do you differentiate #f(x)=sqrt(x+2)#?

So we know that

Derivating both sides we have

Evaluate the limit of the factors we just put in evidence

(This is actually called the product rule and is widely used for more complex functions)

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

To differentiate the function ( f(x) = \sqrt{x+2} ) using the limit definition of the derivative, follow these steps:

- Start with the limit definition of the derivative: [ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]
- Substitute the function ( f(x) = \sqrt{x+2} ) into the formula.
- Expand and simplify the expression.
- Apply the limit as ( h ) approaches 0.

By following these steps, you can find the derivative of the function ( f(x) = \sqrt{x+2} ) using the limit definition.

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

- How do you find the equation of a line tangent to the function #y=ln(-x)# at (-2,ln2)?
- What is the equation of the line normal to # f(x)=ln(x+xe^(3x))# at # x=2#?
- What is the equation of the line normal to # f(x)=1/(e^x+4)# at # x=6#?
- How do you find the equation of the tangent to the curve #y=x^2+2x-5# that is parallel to the line #y=4x-1#?
- How do you find the average rate of change of the function #f(x)=4 ·x^2 + 2 ·x−4# over the interval [3, 3.17]?

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