Question

Derive a função g(x)=ln(2-x) + [e^3x / (e^x + 1)] com sua derivada em x=0

Answer 1

g(x) = ln(2-x) + [e^3x / (e^x+1) ] 

g'(x) = [1 / (2-x) *-1] + [3e^3x*(e^x+1) - (e^x*e^3x)] / [(e^x+1)]²

g'(x) = [-1 / (2-x) ] + (3e^4x+3e^3x - e^4x) / [(e^x+1)]²

g'(x) = 1 / (x-2) + (2e^4x+3e^3x) / [(e^x+1)]²

g'(0) = 1 / (0-2) + (2e^4*0+3e^3*0) / [(e^0+1)]²

g'(0) = 1 / -2 + (2e^0 + 3e^0) / (1+1)²

g'(0) = -1/2 + (2+3) / (2)²

g'(0) = -1/2+5/4

g'(0) = -2/4+5/4

g'(0) = 3/4