Calculus

# Implicit Differentiation - Rational functions

If $\frac { x ( x - 6y) } { 5 - 4 y^ 2 } = 1,$ what is $\displaystyle \frac{dy}{dx}?$

If $\frac{ 3 x ^2 + 7 xy^2 } { 8 + 5 y^3 } = 1$, what is $\displaystyle \frac{dy}{dx}?$

If point $(1,a)$ with $a>0$ lies on the curve $\frac{y}{x}-\frac{9x}{y}=8,$ what is the derivative $\displaystyle \frac{dy}{dx}$ of the curve at the point?

Given $\frac{(x^2+y^2-11x)^2}{x^2+y^2}=4,$ what is the value of $\displaystyle \frac{dy}{dx}$ when $x=0$ and $y=2 ?$

If $\frac{6x-y^3}{y+x^2}=x+4,$ what is $\displaystyle \frac{dy}{dx}?$

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