# 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.

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