Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 207852 by hardmath last updated on 28/May/24

Answered by MM42 last updated on 28/May/24

$$y(y+x+2)=x^2$$$$y^2+xy+2y-x^2=0=f(x,y)$$$$x=4\Rightarrow y^2+6y-16=0\Rightarrow y=2$$$$\frac{dy}{dx}=-\frac{f_x^{{}^{\prime }}}{f_y^{\prime }}=\frac{2x-y}{2y+x+2}$$$$\stackrel{x=4,y=2}{\Rightarrow }=\frac{8-2}{4+4+2}=\frac{6}{10}=\frac{3}{5}✓$$$$$$

Commented by hardmath last updated on 28/May/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

Answered by A5T last updated on 29/May/24

$$x^2=y(y+x+2)\Rightarrow x^2=y^2+xy+2y$$$$\frac{d}{dx}\left(x^2\right)=\frac{d}{dx}\left(y^2\right)+\frac{d}{dx}\left(xy\right)+2\frac{d}{dx}\left(y\right)$$$$2x=2y\frac{dy}{dx}+x\frac{dy}{dx}+y+\frac{2dy}{dx}$$$$\Rightarrow \frac{dy}{dx}=\frac{2x-y}{2y+x+2}\Rightarrow f^{\prime }\left(x\right)=\frac{2\left(4\right)-2}{2\left(2\right)+4+2}=\frac{6}{10}=\frac{3}{5}$$

Commented by hardmath last updated on 29/May/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com