Question

I’m in AP Calculus AB and can’t figure this out. Can you help me solve this?

Answer 1

We need to derivate the next given function:

`f(x)=2x-x^2\tan x`

First, we have a subtraction, which means that we can derivate both expressions separately:

`(d)/(dx)f(x)=(d)/(dx)(2x)-(d)/(dx)(x^2\tan x)`

For 2x:

`(d)/(dx)(2x)=2`

for x²tanx, the expression represents a multiplication. Therefore, we use the next rule:

`(d)/(dx)(f\cdot g)=(d)/(dx)f\cdot g+f\cdot(d)/(dx)g`

Then:

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

The whole derivate would be:

`(d)/(dx)f(x)=2-(2x\tan x+x^2\sec ^2(x))`

Simplify the signs for the expression:

`(d)/(dx)f(x)=2-2x\tan x-x^2\sec ^2(x)`