Find y' if $\displaystyle sin(2xy)+cos^2(xy)=x^2y^2+3y^2.$
I tried using Implicit Differentiation, but the answer I got was all complicated & I can't simplify it.
The derivatives of the terms on the left side are as follows:
1st term: $\displaystyle cos(2xy)\frac{d}{dx}(2xy)=(2y+2xy')cos(2xy)$
2nd term: $\displaystyle \frac{d}{dx}cos^2(xy)=2cos(xy)\frac{d}{dx}cos(xy)$
See if you can find the derivative $\displaystyle \frac{d}{dx}cos(xy)$.
Is everything I've done so far consistent with what you've attempted?
Chain rule, just as e^i*pi said. Always remember to use the chain rule whenever you see a function in the parenthesis. If it isn't just $\displaystyle x$, then you have to apply the chain rule. In this case, you have to apply a combination of the chain rule and implicit differentiation. So try to find the derivative $\displaystyle \frac{d}{dx}cos(xy)$
So do you understand how I found the derviative of $\displaystyle cos^2(xy)$
???
That one is kind of confusing. Other than that, the right side of the equation is very basic. I'm sure you can figure that out. So now you just have to solve for $\displaystyle y'$.