# What is the derivative of #sqrt x^2#?

##### 2 Answers

#### Explanation:

first rewrite

now differentiate using the chain rule :

It is usual to give answer in the same form as question.

Assuming the question is asking

#### Explanation:

The definition of

#d/dx(x) = d/dx(x^1) = (1)x^(1-1) = (1)(x^0) = (1)(1) = 1#

If the problem were instead asking

#d/dx(sqrt(x)) = d/dx(x^(1/2)) = (1/2)x^(1/2 - 1) = (1/2)x^(-1/2) = 1/(2x^(1/2))#

#=1/(2sqrtx)#