1. ## D(x)

If $y=\frac{x^2}{2}+\frac{x\sqrt{x^2+1}}{2}+\ln{\sqrt{ x+\sqrt{x^2+1}}$ prove this

$2y=x\frac{d(y)}{d(x)}+\ln\frac{d(y)}{d(x)}$ In this case i substitute $x=tanx$ but after the solving it become more tough.please help me>>>>>>

2. ## Re: D(x)

Have you thought to work out \displaystyle \begin{align*} \frac{dy}{dx} \end{align*}?

3. ## Re: D(x)

$y=\frac{tan^2x}{2}+\frac{secxtanx}{2}+\ln[\sqrt{secx+tanx}] \\ \frac{d(y)}{dx}=sec^2xtanx+\frac{sec^3x+secxtanx}{ 2}+\frac{secx(secx+tanx)}{2(secx+tanx)}$

after that I cannot arrange what ther ask>>>>>>

4. ## Re: D(x)

I don't know why you're substituting tan(x), or ANY other function for that matter. Just take the derivative...