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 \(\displaystyle \frac{dy}{dx}?\)