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10 cards from this deck
dydx\frac{dy}{dx}dxdy
Finding derivatives where xxx and yyy are functions of parameter ttt
dydx=dydtdxdt\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}dxdy=dtdxdtdy
d2ydx2=ddt(dydx)dxdt\frac{d^2y}{dx^2} = \frac{\frac{d}{dt}(\frac{dy}{dx})}{\frac{dx}{dt}}dx2d2y=dtdxdtd(dxdy)
Slope, concavity, and other curve properties
−1m-\frac{1}{m}−m1 where mmm is gradient of tangent
y−y1=m(x−x1)y - y_1 = m(x - x_1)y−y1=m(x−x1)
Differentiate x=f(t)x=f(t)x=f(t) and y=g(t)y=g(t)y=g(t) w.r.t. ttt
Eliminate parameter ttt from equations
1dxdt\frac{1}{\frac{dx}{dt}}dtdx1 (reciprocal)
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