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## Implicit Differentiation

Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.

#### Challenge Quizzes

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

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