Question

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

Answer 1

Taking the derivative of both sides with respect to
`x` 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`:

`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`.