Please help Calculus The graph of x^2=-2+y+5cosy is shown for y=11, find the derivative dy/dx

Question

asked Jun 13, 2019 2.1k views

1 Answer

Einarmagnus · Answer 1 · 2019-06-17T13:43:10+0000

Taking the derivative of both sides with respect to
gives

$(\mathrm d)/(\mathrm dx)[x^2]=(\mathrm d)/(\mathrm dx)[-2+y+5\cos y]$

$\implies2x=(\mathrm dy)/(\mathrm dx)-5\sin y\,(\mathrm dy)/(\mathrm dx)$

$\implies(\mathrm dy)/(\mathrm dx)=(2x)/(1-5\sin y)$

When
y=11 , we have two possible values of
:

$x^2=-2+11+5\cos11\implies x=\pm√(9+5\cos11)\approx\pm3.004$

so we have two possible values
$(\mathrm dy)/(\mathrm dx)\approx\pm1.001$ .