# How do you find the derivative of #sqrt(x+7)#?

Solution:

God bless....I hope the explanation is useful

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

To find the derivative of ( \sqrt{x+7} ), you can use the power rule for differentiation, which states that the derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ), where ( n ) is any real number.

Apply the power rule to ( \sqrt{x+7} ):

- Rewrite ( \sqrt{x+7} ) as ( (x+7)^{\frac{1}{2}} ).
- Differentiate ( (x+7)^{\frac{1}{2}} ) using the power rule.
- Apply the power rule: ( \frac{d}{dx}(x+7)^{\frac{1}{2}} = \frac{1}{2}(x+7)^{-\frac{1}{2}} ).
- Simplify the expression to obtain the derivative.

So, the derivative of ( \sqrt{x+7} ) with respect to ( x ) is ( \frac{1}{2\sqrt{x+7}} ).

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

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