Calculus
# Implicit Differentiation

If $\sqrt[3]{x^2}+\sqrt[3]{y^2}=4,$ what is $\displaystyle \frac{dy}{dx}?$

If $x=y\sqrt{11+y}$, what is $\displaystyle \frac{dy}{dx}?$

Find $\displaystyle \frac{dy}{dx}$ for $7\sqrt{x}+6\sqrt{y}=13y^2$ at the point $(1,1).$

Given $f(x)=\sqrt[3]{\frac{x}{x^2+124}},$ what is the value of $f'(1)?$

If $\sqrt{3x}+\sqrt{y}=\sqrt{5}$, what is $\displaystyle \frac{dy}{dx}?$