Question

Find dy/dx if f(x) = (x + 1)^(2x)

Answer 1

method one
take the log
take the derivative of the log after "simplifying using property of the log
then multiply your result by the original function

Answer 2

method two
rewrite \[f(x)=(x+1)^{2x}\] as, by definition \[\large e^{2x\ln(x+1)}\] then take the derivative of that using the chain rule
all the actual work will be the same

Answer 3

if you do it both ways you see that the real work is finding the derivative of \[2x\ln(x+1)\] using the product rule

Answer 4

you good from there?

Answer 5

I got (2ln(x+1)+2x/x+1)(x-1)^(2x)

Answer 6

me too

Answer 7

thank you so much!

Answer 8

yw