anonymous
  • anonymous
if f(x)= (3sqrtX)(X^3 -2sqrtX +6) find f'(x)
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
do we assume X = x ?
anonymous
  • anonymous
yes
amistre64
  • amistre64
product rule it then and youll be good

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anonymous
  • anonymous
Take the derivative of f'(x). Use product rule along with chain rule. f'(x)=f'(x)g(x) + f(x)g'(x).
anonymous
  • anonymous
I've tried that several times. I just need an answer.
amistre64
  • amistre64
(3sqrtX)'(X^3 -2sqrtX +6)+(3sqrtX)(X^3 -2sqrtX +6)' \(\cfrac{3}{2\sqrt{x}}\) (X^3 -2sqrtX +6)+ \(3\sqrt{x}\ (3x^2 -\cfrac{1}{\sqrt{x}})\)
amistre64
  • amistre64
\[\frac{3x^3}{2\sqrt{x}}-3+\frac{9}{\sqrt{x}}+9x^2\sqrt{x}-3\]
anonymous
  • anonymous
marmots make sure to regard the sqrt(x) as (x)^1/2. It makes it easier to integrate. Just a tip.
anonymous
  • anonymous
I mean to take the derivative!!
anonymous
  • anonymous
Thanks guys, I appreciate it.
amistre64
  • amistre64
yep, might need to simplify some more, but im pretty sure thats the brunt of it

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