find the derivative of 1. tan^2 x^2 2. sec 2/3 x^3?

VTPETERS2002

5 years ago

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

Explanation:
y=tan2(2x)

First, remember the convention for trigonometric functions:

y=tan2(2x)=(tan(2x))2

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

dydx=2(tan(2x))⋅ddx(tan(2x))
=2tan(2x)⋅sec2(2x)⋅ddx(2x)
=2tan(2x)⋅sec2(2x)⋅(2)
=4tan(2x)sec2(2x)