# What is the second derivative of #f(x)= sec^2x#?

##### 1 Answer

Jan 28, 2016

#### Explanation:

To find the first derivative, we will have to use the chain rule on the second power.

Use the rule that

Thus, we see that

#f'(x)=2secx*d/dx(secx)#

#f'(x)=2secx*secxtanx#

#f'(x)=2sec^2xtanx#

To find the second derivative, we will have to use the product rule.

#f''(x)=2tanxd/dx(sec^2x)+2sec^2xd/dx(tanx)#

Note that we already know that

This gives us

#f''(x)=2tanx(2sec^2xtanx)+2sec^2x(sec^2x)#

#f''(x)=4tan^2xsec^2x+2sec^4x#