Imagine I have a Temperature / Time graph which is plotted by using the function y=sin(x).

In this graph X axes represents 'the time'(in seconds) and Y axes represents 'Temperature'(calcius).

How can i draw temperature change rate graph which is X axes represents 'the time' (in seconds) again but Y axes will represent Temperature/Seconds.

How can i find the function which will draw this temperature change rate graph?

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    $\begingroup$ differentiate $sin x$ to get $cos x$ and plot that $\endgroup$ – David Quinn Jan 25 '19 at 18:01

I'm guessing that you're not yet familiar with calculus.

A basic operation of calculus is differentiation. This takes a function $f(x)$ and produces another function $f'(x) $ for the slope of a graph of $y=f(x)$ at each point. This slope can also be seen as the rate of change of $f(x)$. It's known as the derivative of $f(x)$, and often represented as $\frac{dy}{dx}$.

Originally $dy$ and $dx$ were thought of as infinitely small changes in $y$ and $x$, but nowadays $\frac{dy}{dx}$ is defined slightly differently to stop it meaning $\frac00$.

The first example you encounter is usually $y=x^2$, for which $\frac{dy}{dx}=2x$.

What you're asking for is the derivative—the rate of change—of $sin(x)$. This turns out to be $cos(x)$, so that's what your rate-of-change graph would need to plot.


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