Question

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

Answer 1

take logs on both sides and see where you go :p

use implicit differentiation

Answer 2

\[let f(x)=y\]
\[y=\left( x+1 \right)^{2x}\]
ln y=2xln(x+1)
diff

Answer 3

i got f '(x) = 2 (x+1)^(2 x-1) (x+(x+1) log(x+1))

Answer 4

\[\frac{ 1 }{ y }\frac{ dy }{ dx }=2x \times \frac{ 1 }{ x+1 }+2 \ln \left( x+1 \right)\]
\[\frac{ dy }{ dx }=y \left[ \frac{ 2x }{ x+1 }+2\ln \left( x+1 \right) \right]\]
replace the value of y

Answer 5

I got the same result Chris :)
I'm pretty sure that's right.

Answer 6

thanks guys :)