Homework SourseFind and equation of the tangent line to the curve yxex1ex a
Find and equation of the tangent line to the curve y=xe^x/1+e^x at x=0
Solution
take derivative at x=0
y\' = (1 + ex)[ xex + ex ] - [ xex ] [ ex ] / [1 + ex]2
y\' = (2)[ 1 ] - 0 / 4
y\' = 1/2
equation of line passing through (0 , 0) with slope 1/2
y = x/2 answer !!!
![Find and equation of the tangent line to the curve y=xe^x/1+e^x at x=0Solutiontake derivative at x=0 y\' = (1 + ex)[ xex + ex ] - [ xex ] [ ex ] / [1 + ex]2 y\'](/WebImages/27/find-and-equation-of-the-tangent-line-to-the-curve-yxex1ex-a-1072777-1761562197-0.webp "Find and equation of the tangent line to the curve y=xe^x/1+e^x at x=0Solutiontake derivative at x=0 y\' = (1 + ex)[ xex + ex ] - [ xex ] [ ex ] / [1 + ex]2 y\'")
