ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: suskieanna on November 18, 2018, 10:08:09 am

Title: Anyone help me with this question plz
Post by: suskieanna on November 18, 2018, 10:08:09 am: Can anyone help me with this question? I spent lots of time but I can't just do this question at all... so frustrated...
Title: Re: Anyone help me with this question plz
Post by: AlphaZero on November 18, 2018, 11:36:09 pm: $\begin{align*} \frac{dy}{dx}&=2 \left(x+\sqrt{x^2+1}\right) \left(1+\frac{1}{2}\left(x^2+1\right)^\frac{-1}{2}\cdot 2x\right)\\<br />&=2 \left(x+\sqrt{x^2+1}\right) \left(1+\frac{x}{\sqrt{x^2+1}}\right)\\<br />&=2 \left(x+\sqrt{x^2+1}\right) \cdot \frac{\sqrt{x^2+1}+x}{\sqrt{x^2+1}}\\<br />&=\frac{2\left(x+\sqrt{x^2+1}\right)^2}{\sqrt{x^2+1}}\\<br />&=\frac{2y}{\sqrt{x^2+1}}\end{align*}$

Hope this helps. Have to use the chain rule twice :)