Question

differentiate log(x^2 sinx/2x+1)

Answer 1

Answer:

The answer is $\dfrac{2}{x}+\cot x-\dfrac{2}{2x+1}$

Step-by-step explanation:

Let

    $y=\log(\dfrac{x^2\sin x}{2x+1})=2\log (x)+\log (\sin x)-\log(2x+1)$

Using logarithm formulae

$\Rightarrow \dfrac{dy}{dx}=2(\frac{1}{x})+\dfrac{1}{\sin x}(\cos x)-\dfrac{1}{2x+1}(2)$

          $=\dfrac{2}{x}+\cot x-\dfrac{2}{2x+1}$