# How do you find the derivative of #sqrt(x^2+1)#?

##### 2 Answers

Use implicit differentiation on the left hand side of the equation and ordinary differentiation on the right hand side of the equation.

#### Answer:

Use the chain rule and the power rule.

#### Explanation:

The power rule says that

The chain rule, when combined with the power rule (sometimes called "the general power rule" says that

So

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

# = 1/2 (x^2+1)^(-1/2)* (2x)#

# = x/(x^2+1)^(1/2)#

# = x/(sqrt(x^2+1)#

The differentiation is sped up considerably by learning the

After this is learned, we can simply write