Question

how to differentiate (a+be^x)/(ae^x+b) to become (b^2-a^2)e^x/(ae^x+b)^2

Answer 1

d dx of (a+be^x)/(a e^x +b) = ( (ae^x+b)(be^x)-(a+be^x)(ae^x))/(ae^x+b)^2
= (abe^2x+b^2e^x - a^2 e^x - ab e^2x)/ (ae^x+b)^2
= (b^2 e^x - a^2 e^x)/ (ae^x+b)^2
= (b^2-a^2)e^x/(ae^x+b)^2

Answer 2

thank you