Question

How do you take the derivative of `y=tan^2(2x)`?

Answer 1

Use the power rule, the derivative of tangent and the chain rule (twice).

Explanation:

`y=tan^2(2x)`

First, remember the convention for trigonometric functions:

`y=tan^2(2x) = (tan(2x))^2`

So the outermost function is the square. Use the power and chain rules to get:

`dy/dx = 2(tan(2x)) * d/dx(tan(2x))`

`= 2tan(2x) * sec^2(2x) * d/dx(2x)`

`= 2tan(2x) * sec^2(2x) * (2)`

`= 4tan(2x)sec^2(2x)`