ddx(uv)= v dudx-u dvdxv2 v 0 Keep the subtraction order when applying the quotient rule. Example Differentiate y= x2+13x-1 with respect to x, where x!= 13. dydx = (3x-1)(2x)-(x2+1)(3)(3x-1)2 = 6x2-2x-3x2-3(3x-1)2 = 3x2-2x-3(3x-1)2

\(\dfrac{\mathrm{d}}{\mathrm{d}x}\left(\dfrac uv\right)=\dfrac{v\dfrac{\mathrm{d}u}{\mathrm{d}x}-u\dfrac{\mathrm{d}v}{\mathrm{d}x}}{v^2}\qquad v\ne0\)

Keep the subtraction order when applying the quotient rule.

Differentiate \(y=\dfrac{x^2+1}{3x-1}\) with respect to \(x\), where \(x\ne\dfrac13\).

\(\dfrac{\mathrm{d}y}{\mathrm{d}x}\)\({}=\dfrac{(3x-1)(2x)-(x^2+1)(3)}{(3x-1)^2}\)\({}=\dfrac{6x^2-2x-3x^2-3}{(3x-1)^2}\)\({}=\dfrac{3x^2-2x-3}{(3x-1)^2}\)

Quotient Rule

Quotient Rule

Video Solution: