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

Question

18922 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-28T22:16:18

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

$y=tan^2(2x)$

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:

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

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

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

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

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