derivative of composite function

[PTstudent]

Hello again,

I am stuck on a problem where I have to find the derivative g(x) = (2+(x^2+1)^4)^3 so far I have 3(2+(x^2+1)^4)^2 (4)(x^2+1)^3(2x) I do not know where to go from here. Would I multiply the 3 to out to get (6+3(x^2+1))^4? I am almost sure I cannot do that. Any help is greatly appreciated

J

 

[wjm11]

find the derivative g(x) = (2+(x^2+1)^4)^3 so far I have 3(2+(x^2+1)^4)^2 (4)(x^2+1)^3(2x)

Your derivative looks okay. You can clean it up a little by combining the "3", the "4", and the "2x" factors into 24x. Make sense?

 

[pka]

find the derivative g(x) = (2+(x^2+1)^4)^3 so far I have 3(2+(x^2+1)^4)^2 (4)(x^2+1)^3(2x) I do not know where to go from here. Would I multiply the 3 to out to get (6+3(x^2+1))^4?

If you use LaTeX it makes it readable.
[TEX]g(x)=(2+(x^2+1)^4)^3[/TEX] gives \(\displaystyle g(x)=(2+(x^2+1)^4)^3\)

[TEX]g'(x)=3(2+(x^2+1)^4)^2[4(x^2+1)^3(2x)][/TEX] gives

\(\displaystyle g'(x)=3(2+(x^2+1)^4)^2[4(x^2+1)^3(2x)]\)