Question

x^2y+x+sin^2y=4 how can I find the derivative implicitly?

Answer 1

treat both x and y as variables.

if you take the derivative with respect to x you have
\[ \frac{d}{dx} x = \frac{dx}{dx}= 1 \\
\text{ and }\\
\frac{d}{dx} y = \frac{dy}{dx} \]

use those ideas and the usual "rules": chain rule, derivative of a product, etc.