I solved a few more differentiation problems, but got stuck on the following questions:
Find an expression in tems of x and y for dy/dx, given that:
(x-y)^4=x+y+5
and
((xy)^0.5)+x+y^2=0
Implicit differentiation should be your watchword.Originally Posted by Showcase_22
$\displaystyle
\frac{d}{dx}(x-y)^4=\frac{d}{dx}(x+y+5)
$
so:
$\displaystyle
4(x-y)^3 \left(1-\frac{dy}{dx}\right)=1+\frac{dy}{dx}
$.
Now rearrange into the required form.
RonL
$\displaystyle \left ( \frac{1}{2} \frac{1}{\sqrt{xy}} \right ) \cdot \left ( y + x \frac{dy}{dx} \right ) + 1 + 2y \frac{dy}{dx} = 0$Originally Posted by Showcase_22
where the first set of parenthesis is the $\displaystyle \frac{df}{dg}$ and the second set is the $\displaystyle \frac{dg}{dx}$.
All that's left is to solve for $\displaystyle \frac{dy}{dx}$. I leave it to you. Please feel free to post if you have any difficulties with it.
-Dan