Question

1.) Find the derivative of ((x + 3)/e^x) ^ (Log e X)

2.) T/F (log e X)' = (log e |x|)'

3.) T/F (Log e 7x)' = (log e x)'

4.) Find the derivative of e^(log e 7x)

Answer 1

y = ((x+3)/e^x)^lnx
wow!
lny = lnx(ln(x+3)-ln(e^x))
= lnx(ln(x+3)-1)
1/y y' = 1/x (ln(x+3)-1) + lnx*1/(x+3)
y' = y(ln(x+3)/x - 1/x + lnx/(x+3))
Now you can massage that in many ways.

Answer 2

#2 since lnx is not defined for x<0, I'd say False

#3 since ln 7x = ln7 + lnx, I'd say True

#4 7 (why?)