Calculus

Implicit Differentiation

Implicit Differentiation - Rational functions

         

If x(x6y)54y2=1,\frac { x ( x - 6y) } { 5 - 4 y^ 2 } = 1, what is dydx?\displaystyle \frac{dy}{dx}?

If 3x2+7xy28+5y3=1 \frac{ 3 x ^2 + 7 xy^2 } { 8 + 5 y^3 } = 1 , what is dydx?\displaystyle \frac{dy}{dx}?

If point (1,a)(1,a) with a>0a>0 lies on the curve yx9xy=8,\frac{y}{x}-\frac{9x}{y}=8, what is the derivative dydx\displaystyle \frac{dy}{dx} of the curve at the point?

Given (x2+y211x)2x2+y2=4,\frac{(x^2+y^2-11x)^2}{x^2+y^2}=4, what is the value of dydx\displaystyle \frac{dy}{dx} when x=0x=0 and y=2?y=2 ?

If 6xy3y+x2=x+4,\frac{6x-y^3}{y+x^2}=x+4, what is dydx?\displaystyle \frac{dy}{dx}?

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