Question

How to determine the slope of any point x for the function 5÷(2+x)?

Answer 1

This is the derivative.

`y = 5/(2 + x) = 5(2+ x)^-1`

We now find the derivative WRT x using the chain rule. Let `u = x +2` and `y = 5u^-1`. Then `(du)/(dx) = 1` and `dy/(du) = -5u^(-2)`.

Thus

`dy/dx = (dy)/(du) * (du)/(dx) = -5u^(-2) = -5(x + 2)^(-2)`

Thus the slope of the tangent line at any value of `x` is given by `-5(x+ 2)^(-2)`

Hopefully this helps!