what is the use of derivatives Can any one explain me what is the use of derivatives in real life. When and where we use derivative, i know it can be used to find rate of change but why?. My logic was in  real life most of the things we do are not linear functions and derivatives helps to make a real life functions into linear.
eg converting parabola into a linear function $x^{2}\rightarrow 2x$
but then i find this; derivation of $\sin{x}\rightarrow \cos{x}$
why we cant use $\sin{x}$ itself to solve the equation. whats the purpose of using its derivative $\cos{x}$.
Please forgive me if i have asked a stupid questions, i want to improve my fundamentals in calculus.

There can be also economic interpretations of derivatives. For example, let's assume that there is a function which measures the utility from consumption.
$U(C)$ where $C$ is the consumption. It is straightforward to say that your utility increases with consumption. This means that when you increase your consumption one unit marginally, you will have an increase of your utility, which you can find it by taking derivative of this function. (it is not a partial derivative because the only argument in your function is consumption.)
So you will have ;
$\frac{dU(C)}{dC} > 0 $
By intuition, the increase of the utility will be less more you consume. Let's take the simplest example, you have one coke and you drunk it. The second coke you will drink just after will provide you utility but less. The increase of your utility will be less fast more you consume. This one can be formulated by the second derivative of the utility function as follows ;
$\frac{d^{2}U(C)}{dC^{2}} < 0$
