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10 cards from this deck
Differentiating functions written as fraction of two functions
F′(x)=g(x)f′(x)−f(x)g′(x)[g(x)]2F'(x) = \frac{g(x)f'(x) - f(x)g'(x)}{[g(x)]^2}F′(x)=[g(x)]2g(x)f′(x)−f(x)g′(x)
Denom × deriv of num - num × deriv of denom, over denom squared
g(x)≠0g(x) \neq 0g(x)=0
dydx=vdudx−udvdxv2\frac{dy}{dx} = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^2}dxdy=v2vdxdu−udxdv
sec2θ\sec^2 \thetasec2θ
Using the product rule and chain rule together
Order in numerator crucial: g⋅f′−f⋅g′g \cdot f' - f \cdot g'g⋅f′−f⋅g′ (not reversed)
The square of the denominator: [g(x)]2[g(x)]^2[g(x)]2
Cannot do this; must use quotient rule
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