Question

Differentiate and simplify please help??

Answer 1

Use logarithmic differentiation:

`lny= ln(2x + 1)^x`

`lny = xln(2x + 1)`

Now differentiate with respect to `x`.

`1/y(dy/dx) = 1(ln(2x + 1)) + x(2/(2x +1))`

`1/y(dy/dx) = ln(2x+ 1) + (2x)/(2x+ 1)`

`dy/dx = y(ln(2x+ 1) + (2x)/(2x + 1))`

`dy/dx = (2x + 1)^x(ln(2x +1) + (2x)/(2x + 1))`

Hopefully this helps!