Implicit Differentiation Part 2

Rational

100

xy^2=5

\frac{dy}{dx}=\frac{-y}{2x}

200

x^2y^2=2

\frac{dy}{dx}=\frac{-y}{x}

300

3x+5y=xy

\frac{dy}{dx}=\frac{3-y}{x-5}

400

\sqrt{y}=1/x

\frac{dy}{dx}=\frac{-2\sqrt{y}}{x^2}

500

x^2-y^2=x

\frac{dy}{dx}=\frac{1-2x}{-2y}

Quadratic

100

x=3+y^2

\frac{dy}{dx}=\frac{1}{2y}

200

y-x=y^2

\frac{dy}{dx}=\frac{1}{1-2y}

300

\sqrt{y+1}=10-x

\frac{dy}{dx}=-2\sqrt{y+1}

Trig

100

x+y=\cosy

\frac{dy}{dx}=\frac{-1}{1+\siny}

200

x+y=siny

\frac{dy}{dx}=\frac{1}{cosy-1}

300

ycosy=x^3

\frac{dy}{dx}=\frac{3x^2}{cosy-ysiny}

400

tan(y^2)=x-y

\frac{dy}{dx}=\frac{1}{2ysec^2(y^2)+1}

500

tany+xy=20

\frac{dy}{dx}=\frac{-y}{sec^2y+x}

600

siny+cosy=tanx

\frac{dy}{dx}=\frac{sec^2x}{cosy-siny}

e/Log

100

e^ye^x=ln(e^10)

\frac{dy}{dx}=-1

200

x^2-y^2=loge

\frac{dy}{dx}=\frac{x}{y}

300

ln(y^2)=4(x+y)

\frac{dy}{dx}=\frac{4}{\frac{2}{y}-4}

400

lny=2xy

\frac{dy}{dx}=\frac{2y}{\frac{1}{y}-2x}

500

3e^y+x=y

\frac{dy}{dx}=\frac{1}{1-3e^y}

600

e^{x+y}=y+1

\frac{dy}{dx}=\frac{e^{x+y}}{1-e^{x+y}}

Linear

100

\frac{5}{y}=10

\frac{dy}{dx}=0

200

\frac{x+y}{y}=-3

\frac{dy}{dx}=-\frac{1}{4}

300

3x-3y=x+2y

\frac{dy}{dx}=\frac{2}{5}

400

\frac{x-y}{x}=-16

\frac{dy}{dx}=17

Mysterious

100

\frac{siny}{15}=x^3

\frac{dy}{dx}=\frac{45x^2}{cosy}

200

\pi^2=5x^2+\frac{6}{y}

\frac{dy}{dx}=\frac{5xy^2}{3}

300

\frac{x}{y}=x^2

\frac{dy}{dx}=\frac{2xy^2-y}{-x}

400

x^2+y^2=y

\frac{dy}{dx}=\frac{2x}{1-2y}

500

e^{y}=y^{2}+x^{2}

\frac{dy}{dx}=\frac{2x}{e^y-2y}

600

(xy)^3=8-x

\frac{dy}{dx}=\frac{-1-3x^2y^3}{3x^3y^2}