Question

Little bit stuck on derivatives.
So I have the problem:
"Find dy/dx of [y]+[√(xy)]=5"
Im just a bit confused on what to do with "[√(xy)]".
I think I'm supposed to do "(dy/dx)+(1/2)[(xy)^-1/2]=0
And then do the product rule for xy, but I feel like it's wrong. Could anyone help explain what i'm supposed to do with the blasted square root of XY.

Answer 1

yes you're right.

Answer 2

So If I try to get the derivitive \[dy/dx + 1/2\sqrt{y+x(dy/dx)} =0\] does that look right?

Answer 3

hmm no \[\huge\rm \frac{dy}{dx} + \frac{1}{2} (xy)^{-\frac{1}{2}} \cdot D~of~(xy)\]
D=derivative
correct ??

(xy)^{-1/2} flip the fraction to get the positive exponent
\[\huge\rm \frac{dy}{dx} + \frac{1}{2} \frac{1}{ (xy)^ \frac{1}{2}} \cdot D~of~(xy)\]
\[\huge\rm \frac{dy}{dx} + \frac{1}{2 \sqrt{xy}}\cdot D~of~(xy)\]

Answer 4

for the chain rule first we apply the power rule and then multiply by the derivaive of inner function,... therefore derivative of xy shouldn't be under the root

Answer 5

btw D of (xy) is correct
it's = y+xdy/dx

Answer 6

thank you you helped a lot. I might just yet get through this unit alive.

Answer 7

you're welcome. derivatives are not really difficult. just practice with all these rules then..you will be fine!! :)