# How can I Plot “Change Rate Graph” of Sine Graph

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?

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

## 1 Answer

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.