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

##### 1 Answer

*The derivative of #y = tan(x)sec(x)# with respect to #x# is #(dy)/(dx) = sec^3(x) + sec(x)tan^2(x)#*

To perform this differentiation, we will need to use the **Product rule**, which states that given the product of two functions,

Or, more simply:

By setting

The derivative of the function

This equation can be further simplified if desired...

At this point, if desired, one can manipulate trigonometric identities, specifically

or

Source for Trigonometric derivative proofs:

"Proofs: Derivative Trig Functions." *Math .com*. Math .com, 2000-2005. Web. 28 August 2014.

*Spacing included to accommodate Socratic website coding format.*