# Thread: Whats the Order?? derivative mess..

1. ## Whats the Order?? derivative mess..

Hi!

I've got a little problem solving this:

f(x)=tan^3(4x+x^2)

(its a cubed tangent..)

Can't find f' ...
well I do get f'(x)=3.tan^2(4x+x^2)*(2x+4)*(1+tan(4x+x^2))
But it dosent sound right to me so have you got any idea whats wrong and how to solve this?

Thank you
charlie

2. Originally Posted by xobiomesh
Hi!

I've got a little problem solving this:

f(x)=tan^3(4x+x^2)

(its a cubed tangent..)

Can't find f' ...
well I do get f'(x)=3.tan^2(4x+x^2)*(2x+4)*(1+tan(4x+x^2))
But it dosent sound right to me so have you got any idea whats wrong and how to solve this?

Thank you
charlie
You have to use the chain rule.

$\displaystyle \frac{\mathrm{d}f(x)}{\mathrm{d}x} = \frac{\mathrm{d}\left(\tan ^3(4x+x^2)\right)}{\mathrm{d}x}$

Let $\displaystyle u=4x+x^2$ then by chain rule: $\displaystyle \frac{\mathrm{d}f(x)}{\mathrm{d}x} = \frac{\mathrm{d}\tan^3 u}{\mathrm{d}u}.\frac{\mathrm{d}u}{\mathrm{d}x}$

NOTE: When differentiating $\displaystyle \frac{\mathrm{d}\tan^3 u}{\mathrm{d}u}$, you will need to use chain rule here too.