Question

I’m in AP Calc AB. Could you help me with this?

Answer 1

We have to find the derivative of:

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

We can separate and derive the terms independently, but for the second term we have to apply the product rule:

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

Then, we can derive f(x) as:

`\begin{gathered} (df)/(dx)=(d(2x))/(dx)-((d(x^2))/(dx)\cdot\tan (x)+x^2\cdot(d(\tan x))/(dx)) \\ (df)/(dx)=2-(2x\cdot\tan (x)+x^2\cdot\sec ^2(x)) \\ (df)/(dx)=-x^2\cdot\sec ^2(x)-2x\cdot\tan (x)+2 \end{gathered}`

Answer: the derivative of f(x) is df/dx = -x²*sec²(x) - 2x*tan(x) + 2