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10 cards from this deck
If f/gf/gf/g, use (g∗f′−f∗g′)/g2(g*f' - f*g')/g^2(g∗f′−f∗g′)/g2 to differentiate.
ddx(uv)=vu′−uv′v2\frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v u' - u v'}{v^2}dxd(vu)=v2vu′−uv′
They are the derivatives of the numerator and denominator.
Identify the functions u(x)u(x)u(x) and v(x)v(x)v(x).
Differentiate each function to find u′(x)u'(x)u′(x) and v′(x)v'(x)v′(x).
Combine and reduce the expression if possible.
dy/dx=(−4x)/(x2−1)2dy/dx = (-4x)/(x^2 - 1)^2dy/dx=(−4x)/(x2−1)2 after applying the quotient rule.
When functions are composite, use both rules together.
It accounts for changes in both numerator and denominator.
Point where the derivative is zero or undefined.
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