Monday, November 27, 2017

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 42

Find the derivative of the function y=xex2(x2+1)10, using log differentiation

lny=ln[xex2(x2+1)10]lny=lnx+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=121x+2x+101x2+1ddx(x2+1)1yy=12x+2x+10x2+12xyy=12x+2x+20xx2+1y=y(12x+2x+20xx2+1)y=(xex2(x2+1)10)(12x+2x+20xx2+1)

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