Question

Find the derivative of the function below.

Answer 1

\[\frac{2 - \ln(x)}{12^{\frac{3}{2}}}\]

Answer 2

the denominator should say \[12x^{\frac{3}{2}}\]

Answer 3

I was just about to say :)

Answer 4

Ive gotten to a cetain point.. but im stuck on the simplifying

Answer 5

certain*

Answer 6

did u use quotient rule?

Answer 7

yeah

Answer 8

Post what you have so far and I'll see if you're close.

Answer 9

du/dx = -1/x
dv/x = 18 x^(1/2)

Answer 10

\[\frac{(12x^{\frac{3}{2}})(-\frac{1}{x}) - \frac{3}{2}(12)x^{\frac{1}{2}}(2 - \ln(x)}{(12x^{\frac{3}{2}})^2}\]

Answer 11

\[{(12x^{3/2})(-1/x)-18x^{1/2}(2-\ln x) \over 12^2x^3}={-48x^{1/2}+18x^{1/2}\ln x \over144x^3}\]

Answer 12

\[-1/(12*x^(5/2))-(1/8)*(2-ln(x))/x^(5/2)\]

that's what maple gave me.

Answer 13

not much left here... factor out 6x^(1/2)
\[{3\ln x-8 \over 24x^{5/2}}\]

Answer 14

ok..on the first one you posted.. where did the 48^1/2 come from??

Answer 15

notice how 12x^(3/2)(-1/x)=-12x^(1/2)
and 2(-18x^(1/2)=-36x^(1/2)
we added those x^1/2 terms in the numerator to get -48x^(1/2)

Answer 16

ah ok

Answer 17

Thank you Turing!!