Question

find dy/dx by implicit differentiation of:
2x^2 + x + xy = 1
and
cos(x) + sqrt(y) = 5

Answer 1

2x^2 + x + xy = 1
derive 2x^2, it is 4x then derive x, it is 1.
derive xy, get y + xy'
and for right side, derivative of 1 it is 0
now can you simplify this

Answer 2

$$\cos x + y^{1/2} = 5 \\
\frac{d}{dx}[\cos x + y^{1/2}] = \frac{d}{dx}[5] \\
-\sin x + \frac{1}{2}y^{-1/2} \frac{dy}{dx} = 0 \\$$
Solve for \( \frac{dy}{dx} \).