SOLUTION: Find an equation of the tangent line to the curve y=e^x/(1+2e^x ) at the point whose x-coordinate is 0. Differentiate f(x)=x^x+e^(x-x^3 )-ln⁡〖(ln⁡〖(3x)〗)〗

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Question 1159793: Find an equation of the tangent line to the curve y=e^x/(1+2e^x ) at the point whose x-coordinate is 0.
Differentiate f(x)=x^x+e^(x-x^3 )-ln⁡〖(ln⁡〖(3x)〗)〗

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

if
find tangent point:



tangent point is: (,)


we need a slope of the tangent line, so find derivative:


apply the Quotient Rule
'..........this simplifies to
'

use given to find the slope of the tangent line

'
'
'
'=> the slope of the tangent line is

tangent line is:
..............use tangent point (,) and the slope



and tangent line is:






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