# 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 =

##### 1 Answer

#### Explanation:

We know that the derivative (w.r.t.

Using the chain rule, the derivative (w.r.t.

So

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