Question

Can someone help me figure out the answer and..possibly show the steps.. to finding the derivative of these 3 questions..

1. f(x)=2(e^x) - x^2

2. f(x)=e^x/(e^x +1)

3. y=10^(√x)

Answer 1

#1. (e^x)' = e^x, so
f' = 2e^x - 2x

#2.
quotient rule:
f' = (e^x(e^x+1) - e^x*e^x)/(e^x+1)^2
= (e^2x + e^x - e^2x)/(e^x+1)^2
= e^x/(e^x+1)^2

or, knowing that e^x/(e^x+1) = 1 - 1/(e^x+1)
f' = e^x/(e^x+1)^2

#3. Recall that (a^u)' = ln a a^u u'

y' = ln 10 10^√x * 1/(2√x) = ln10/(2√x) 10^(√x)

Answer 2

d/dx(1+8/x)*