d dx(uv)=u dv dx+v du dx Example Differentiate y=x2(2x+1)3 with respect to x. Take u=x2 and v=(2x+1)3. dydx =x2 [3(2x+1)2(2) ]+(2x+1)3(2x) =6x2(2x+1)2+2x(2x+1)3 =2x(2x+1)2 [3x+(2x+1) ] =2x(2x+1)2(5x+1)

\(\dfrac{\mathrm d}{\mathrm dx}(uv)=u\dfrac{\mathrm dv}{\mathrm dx}+v\dfrac{\mathrm du}{\mathrm dx}\)

Differentiate \(y=x^2(2x+1)^3\) with respect to \(x\).

\(\dfrac{\mathrm{d}y}{\mathrm{d}x}\)\({}=x^2\bigl[3(2x+1)^2(2)\bigr]+(2x+1)^3(2x)\)\({}=6x^2(2x+1)^2+2x(2x+1)^3\)\({}=2x(2x+1)^2\bigl[3x+(2x+1)\bigr]\)\({}=2x(2x+1)^2(5x+1)\)

Product Rule

Product Rule

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