How to find all possible functions with the given derivative ? If y′=sin(7t), then y = If y′=cos(t/7), then y = If y′=sin(7t)+cos(t/7), then y =
We know that the derivative (w.r.t.
Using the chain rule, the derivative (w.r.t.
If we multiply by the constant
So one possible function with derivative
But there are others.
Indeed, For any (every) constant
Not only that, but due to an important consequence of the Mean Value Theorem, every function that has this derivativs differs from
Similar reasoning leads us to the functions ahose derivative is
Because the derivative of a sum is the sum of the derivatives, every function whose derivative is