# What is the derivative of #y=sec^2(x) + tan^2(x)#?

##### 1 Answer

The derivative of

#4sec^2xtanx#

**Process:**

Since the derivative of a sum is equal to the sum of the derivatives, we can just derive

For the derivative of

#F(x) = f(g(x))#

#F'(x) = f'(g(x))g'(x)# ,

with the outer function being

#f(x) = x^2#

#f'(x) = 2x#

#g(x) = secx#

#g'(x) = secxtanx#

Plugging these into our Chain Rule formula, we have:

#F'(x) = f'(g(x))g'(x)# ,

#F'(x) = 2(secx)secxtanx = 2sec^2xtanx#

Now we follow the same process for the

#f(x) = x^2#

#f'(x) = 2x#

#g(x) = tanx#

#g'(x) = sec^2x#

#F'(x) = f'(g(x))g'(x)# ,

#F'(x) = 2(tanx)sec^2x = 2sec^2xtanx#

Adding these terms together, we have our final answer:

#2sec^2xtanx + 2sec^2xtanx# =

#4sec^2xtanx#