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

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Answer 1 · 2017-03-09T20:53:03

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

Differentiate both sides with respect to $x$ using the product rule:

$d/dx (xsqrt(y+2)) = d/dx 4$

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

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

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

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

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

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