Implicit Differentiation

Implicit Differentiation - Polynomials


What is the slope of the curve 8x2+5y2=r2 8x^2 + 5y^2 = r^2 (where r0)r \neq 0) at a point (x1,y1) (x_{1}, y_{1}) that lies on the curve?

What is the slope of the tangent line of the curve x2=y2 x^2 = y^2 at the point (15,15)? (15, -15)?

If y4=17x,y^{4}=17x, what is dydx?\displaystyle \frac{dy}{dx}?

Determine the slope of the line tangent to the circle (x2)2+(y4)2=32(x-2)^2 + (y-4)^2 = 32 at the point (x,y)=(6,0)(x,y) =(6,0).

If y34y2=x5+3x4,y^3-4y^2=x^5+3x^4, what is dydx?\displaystyle \frac{dy}{dx}?


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