Finding implicit differentiation using power rule.

Question

Original Function: $(\sin(\pi x)+\cos(\pi y))^2 = 2$
Step1: $2(\pi \cos(\pi x) - \pi \sin(\pi y)\frac{dy}{dx})(\sin(\pi x)+\cos(\pi y))$

Step2: $(2\pi \cos(\pi x)-2\pi \sin(\pi y)\frac{dy}{dx})(\sin(\pi x)+\cos(\pi y)$

... and blah blah blah.. Igot tired of writing this in mathjax..

and my answer came out to be dy/dx = $\cos(\pi x)$ / $\sin(\pi y)$

did I do this right?

Answer 1

Ya you are correct. You can actually use the formula of

$$ dy/dx = -F_x/Fy$$

This might be easier.