Find derivative of sec(theta) * tan(theta)

d/dx sec (theta) * d/dx tan (theta)

sec(theta) tan(theta) * sec^2 (theta)


The answer they're looking for is
sec (theta) * [sec^2(theta) + tan^2(theta)]

I'm wondering the conversion process from my answer into their answer.

You need to use a product rule. If you have multiplication of two terms that don't merge, you can consider them as two functions (I've substituted x for theta since I don't have theta on my phone keyboard). f(x)=secx. g(x)=tanx.

Here is the general rule:
y = f(x)•g(x)
y' = f'(x)•g(x) + f(x)•g'(x)

The derivative of the first times the original of the second. Plus the derivative of the second times the original of the first.


You should look up the quotient rule and the chain rule as well since you'll probably have those soon if not in this same assignment.

This post was edited by timmayX on Mar 10 2016 01:12pm

do a timmayX suggested. I just want to add:

be careful with your notation:

d/dx means the derivative with respect to x; and it seems like you want the derivative with respect to θ so use d/dθ