How do you find (dy)/(dx)dydx given xsqrt(y+2)=4xy+2=4?

1 Answer
Mar 9, 2017

dy/dx = -(2(y+2))/xdydx=2(y+2)x

Explanation:

Differentiate both sides with respect to xx using the product rule:

d/dx (xsqrt(y+2)) = d/dx 4ddx(xy+2)=ddx4

sqrt(y+2) + x/(2sqrt(y+2))dy/dx = 0y+2+x2y+2dydx=0

+ x/(2sqrt(y+2))dy/dx = -sqrt(y+2)+x2y+2dydx=y+2

dy/dx = -(2(y+2))/xdydx=2(y+2)x

As x > 0x>0 we can also write it as:

dy/dx = -(2xsqrt(y+2)sqrt(y+2))/x^2 = -(8*sqrt(y+2))/x^2dydx=2xy+2y+2x2=8y+2x2