Calculus 1: Implicit Differentiation

Use implicit differentiation to find $\frac{dy}{dx}$ for the following equation

$x^2 + y^2 = 25 + 5x$

For the following function, find $\frac{dy}{dx}$ by implicit differentiation

$x^2 + 2xy + y^2 = 5$

Use implicit differentiation to take the derivative of $y$ with respect to $x$ for the following equation

$y^5 + 2y = x^2$

Find the tangent line to the curve $xy + \ln{(xy^2)} = 1$ at the point $(1,1)$

Find $\frac{dy}{dx}$ and the slope of the tangent line at $(-2, 1)$ for the curve given by

$2x^2 - 3y^3 = 5$