Implicit Differentiation

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

-\frac{dy}{dx}=\frac{\sqrt[3]{y}}{\sqrt[3]{x}}

-\frac{dy}{dx}=\frac{\sqrt[3]{x}}{\sqrt[3]{y}}

-\frac{dy}{dx}=\frac{\sqrt[3]{y^2}}{\sqrt[3]{x^2}}

-\frac{dy}{dx}=\frac{\sqrt[3]{x^2}}{\sqrt[3]{y^2}}

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

\frac{1}{2\sqrt{11+y}} \left(y \neq -{11}\right)

\frac{3y+22}{2\sqrt{11+y}} \left(y \neq -{11}\right)

1+\frac{1}{2\sqrt{11+y}} \left(y \neq -{11}\right)

\frac{2\sqrt{11+y}}{3y+22} \left(y \neq -\frac{22}{3}\right)

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 $\displaystyle \frac{dy}{dx}?$

\frac{dy}{dx}=-\frac{\sqrt{3y}}{\sqrt{x}}

\frac{dy}{dx}=-\frac{\sqrt{y}}{\sqrt{3x}}

\frac{dy}{dx}=\frac{\sqrt{y}}{\sqrt{3x}}

\frac{dy}{dx}=\frac{\sqrt{3y}}{\sqrt{x}}

Implicit Differentiation - Radical Functions