Find the derivative of the function y=√xex2(x2+1)10, using log differentiation
lny=ln[√xex2(x2+1)10]lny=ln√x+lnex2+ln(x2+1)10lny=lnx12+x2+ln(x2+1)10lny=12lnx+x2+10ln(x2+1)ddxlny=12ddx(lnx)+ddx(x2)+10ddxln(x2+1)1ydydx=12⋅1x+2x+10⋅1x2+1ddx(x2+1)1yy′=12x+2x+10x2+1⋅2xy′y=12x+2x+20xx2+1y′=y(12x+2x+20xx2+1)y′=(√xex2(x2+1)10)(12x+2x+20xx2+1)
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