Question

dy/dx

Answer 1

\[f(x)=\left(2x+1\right)^{\sin(x)}\] you have a choice
you can rewrite this as
\[f(x)=e^{\sin(x)\ln(2x+1)}\] and take the derivative using the chain rule, or
you can take the log, get
\[\sin(x)\ln(2x+1)\] then take the derivative using the product rule, then multiply by the original function

the answers of course will be the same, and also so will the work. either way your job is really to find the derivative of \(\sin(x)\ln(2x+1)\)

Answer 2

dy/dx=2sinx(2x+1)sinx-1 ----Look sinx-1 is power

Answer 3

for which of course you need the product rule. for
\[\frac{d}{dx}[\sin(x)\ln(x)]\]
use \((fg)'=f'g+g'f\) with \(f(x)=\sin(x),f'(x)=\cos(x), g(x)=\ln(2x+1), g'(x)=\frac{2}{2x+1}\)

Answer 4

should i need to take ln both sides