How do we use derivatives in our daily lives How can we use derivatives in our real lives, I know that we have a lot of formulas to find the derivatives of a function,but why do we need them ?

Derivatives are very important for lots of things especially in 
Physics and Engineering. I use derivatives almost every day as an
engineer. 
In my work, I study vibrations of underwater pipelines.  We are 
largely worried about fatigue, where we are trying to figure out how
to build underwater pipelines so that they do not break.
We test a lot of pipes both in pools and in the ocean.  We often
measure strain when we are testing pipes; the strain is how much the
pipe stretches when it vibrates divided by the total length of the
pipe.  Sometimes these vibrations are so small that you can not see
them, but they can cause big damage to the pipe. 
To calculate the fatigue, I need to know how much the pipe is curved.
It turns out that strain is the first derivative of curvature.  So I
can find the curvature and therefore I can solve for the fatigue, and
then I can tell you when your pipe is going to break. 
This is just one example.  Derivatives are used all the time by
scientists, mathematicians, and engineers to solve all sorts of problems. 
