Waste less time on Facebook — follow Brilliant.
×

Help: derivatives

Moderator's edit:

Given that \( x = y + \cfrac 1{y + \cfrac1{y + \cfrac1{y + \cfrac1{y + _\ddots}}}} \).

Show that \( \dfrac{dy}{dx} = 2x^2 + y^2 - 3xy \).

Note by Akhilesh Prasad
6 months, 3 weeks ago

No vote yet
1 vote

Comments

Sort by:

Top Newest

\[x=y+\dfrac 1x \implies 1=x(x-y)\cdots (2)\\ \implies x^2=xy+1\cdots (1)\] Differentiating \((1)\) \[y'=(\dfrac{2x-y}{x})(1)\] Using \((2)\): \[y'=(\dfrac{2x-y}{\not x})(\not x(x-y))\] \[=2x^2-3xy+y^2\] Rishabh Cool · 6 months, 3 weeks ago

Log in to reply

@Rishabh Cool I think the minute i opened the note and saw the moderator's edit, that was when the answer came to me. Kudos to the moderator. Akhilesh Prasad · 6 months, 3 weeks ago

Log in to reply

@Rishabh Cool Thanks a lot. Akhilesh Prasad · 6 months, 3 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...