# How do you find the derivative of the function #f(x)=x+sqrtx#?

Derivative of the function,

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

Being of the old school I will use the Leibnitz notation

I do not like roots in the denominator so lets see if we can get rid of it.

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

To find the derivative of the function ( f(x) = x + \sqrt{x} ):

- Differentiate each term separately.
- For ( x ), the derivative is ( 1 ) since it follows the power rule (( \frac{d}{dx} x^n = nx^{n-1} )).
- For ( \sqrt{x} ), the derivative is ( \frac{1}{2\sqrt{x}} ) using the power rule and the chain rule.
- Combine the derivatives of both terms.
- The derivative of ( f(x) = x + \sqrt{x} ) is ( f'(x) = 1 + \frac{1}{2\sqrt{x}} ).

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