5–8. Calculate dy/dx using implicit differentiation.
sin y+2 = x

Verified step by step guidance

1. Start by differentiating both sides of the equation sin(y) + 2 = x with respect to x. Remember to apply the chain rule when differentiating sin(y).
2. The derivative of sin(y) with respect to x is cos(y) * (dy/dx), since y is a function of x. The derivative of the constant 2 is 0, and the derivative of x is 1.
3. Set up the equation from the differentiation: cos(y) * (dy/dx) + 0 = 1.
4. Isolate dy/dx by rearranging the equation: dy/dx = 1/cos(y).
5. You can also express dy/dx in terms of sec(y) since sec(y) = 1/cos(y). Thus, dy/dx = sec(y).