# Whats the Order?? derivative mess..

• Apr 11th 2009, 03:24 AM
xobiomesh
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
• Apr 11th 2009, 03:48 AM
Air
Quote:

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.