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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.

Polynomials

         

What is the slope of the curve \( 8x^2 + 5y^2 = r^2\) 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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