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



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amistre64
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do we assume X = x ?

marmots
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yes

amistre64
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product rule it then and youll be good

jrodriguez2315
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Take the derivative of f'(x). Use product rule along with chain rule. f'(x)=f'(x)g(x) + f(x)g'(x).

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

amistre64
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(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
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\[\frac{3x^3}{2\sqrt{x}}3+\frac{9}{\sqrt{x}}+9x^2\sqrt{x}3\]

jrodriguez2315
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marmots make sure to regard the sqrt(x) as (x)^1/2. It makes it easier to integrate. Just a tip.

jrodriguez2315
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I mean to take the derivative!!

marmots
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Thanks guys, I appreciate it.

amistre64
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yep, might need to simplify some more, but im pretty sure thats the brunt of it