Question

if f(x)= (3sqrtX)(X^3 -2sqrtX +6) find f'(x)

Answer 1

do we assume X = x ?

Answer 2

yes

Answer 3

product rule it then and youll be good

Answer 4

Take the derivative of f'(x). Use product rule along with chain rule. f'(x)=f'(x)g(x) + f(x)g'(x).

Answer 5

I've tried that several times. I just need an answer.

Answer 6

(3sqrtX)'(X^3 -2sqrtX +6)+(3sqrtX)(X^3 -2sqrtX +6)'

\(\cfrac{3}{2\sqrt{x}}\) (X^3 -2sqrtX +6)+ \(3\sqrt{x}\ (3x^2 -\cfrac{1}{\sqrt{x}})\)

Answer 7

\[\frac{3x^3}{2\sqrt{x}}-3+\frac{9}{\sqrt{x}}+9x^2\sqrt{x}-3\]

Answer 8

marmots make sure to regard the sqrt(x) as (x)^1/2. It makes it easier to integrate. Just a tip.

Answer 9

I mean to take the derivative!!

Answer 10

Thanks guys, I appreciate it.

Answer 11

yep, might need to simplify some more, but im pretty sure thats the brunt of it