derivative
posted by Anoymous on .
How do you find the derivative of
F(x) = root5(3 + 5 x + x^3)?

f(x)=u^k
f'= ku^(k1) du
so here, that does something like this..
I assume root5 means the 1/5 power.
f'= 1/5( )^(4/5) * (5 + 3x^2) 
5/2root(3+5x+x^3) * 5+3x^2=
(5(5+3x^2))/(2root(3+5x+x^2) 
Is that the 5th root of (3+5x+x^3)? If so, you can rewrite it as (3+5x+x^3)^(1/5). You have to use the chain rule to find this derivative. First set (3+5x+x^3)=z. You know have z^(1/5). Take the derivative of this. (1/5)z^(1/51)=(1/5)z^(4/5). Now substitute (3+5x+x^3) back in for z. (1/5)(3+5x+x^3)^(4/5). Take the derivative of the inside, which is (3+5x+x^3). You get (0+5+3x^2)=(5+3x^2). Multiple this with (1/5)(3+5x+x^3)^(4/5). You get (1/5)(5+3x^2)(3+5x+x^3)^(4/5).

Anonymous is wrong, don't use that. bobpursley and I are correct.