Question

If f(x)=the square root of 6x, find f'(x).

Answer 1

\[f(x) = (6x)^{1 \over 2} \]Hint: use power rule to simplify.

Answer 2

if f(x)=6x^1/2 then the derivitive is simply 3x^-1/2

Answer 3

\[ {d \over dx}x^n = nx^{n - 1}\]

Answer 4

fprime=3/\[\sqrt{x}\]

Answer 5

I tried 3x^(-1/2) already but it says it's wrong. I also need to find f'(6).

Answer 6

actually...it's not 3(x)^-1/2
\[\frac{d}{dx} \sqrt{g(x)} \implies \frac {g'(x)}{2\sqrt{g(x)}}\]
so in this case..g(x) is 6x and g'(x) is 6

so you have \[\implies \frac{6}{2\sqrt{6x}}\]
simplify to get the desired answer