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

Question

asked Jan 13, 2023 112k views

1 Answer

Andy Xufuris · Answer 1 · 2023-01-19T10:37:47+0000

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:

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:

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