Calculus
Implicit Differentiation
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 \(\displaystyle \frac{dy}{dx}?\)