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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.

# Implicit Differentiation - Polynomials

What is the slope of the curve $$8x^2 + 5y^2 = r^2$$ (where $$r \neq 0)$$ at a point $$(x_{1}, y_{1})$$ that lies on the curve?

What is the slope of the tangent line of the curve $$x^2 = y^2$$ at the point $$(15, -15)?$$

If $$y^{4}=17x,$$ what is $$\displaystyle \frac{dy}{dx}?$$

Determine the slope of the line tangent to the circle $$(x-2)^2 + (y-4)^2 = 32$$ at the point $$(x,y) =(6,0)$$.

If $$y^3-4y^2=x^5+3x^4,$$ what is $$\displaystyle \frac{dy}{dx}?$$

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