How do you implicitly differentiate x+sqrty=7x+y=7?

2 Answers

dy/dx=2x-14dydx=2x14

Explanation:

Given equation:

x+\sqrty=7x+y=7

differentiating above equation w.r..t xx on both the sides as follows

d/dx(x+\sqrty)=d/dx(7)ddx(x+y)=ddx(7)

d/dx(x)+d/dx\sqrty=0ddx(x)+ddxy=0

1+1/{2\sqrty}dy/dx=01+12ydydx=0

dy/dx=-2\sqrtydydx=2y

dy/dx=-2(7-x)dydx=2(7x)

dy/dx=2x-14dydx=2x14

Jul 27, 2018

dy/dx=-2(7-x)dydx=2(7x).

Explanation:

x+sqrty=7x+y=7.

:. sqrty=7-x.

:. y=(7-x)^2.

:. dy/dx=2(7-x)*d/dx(7-x)=-2(7-x).