# Exponential Graphs => differenciation.gmi You should understand differentiation before reading this section Exponential graphs are those in the form of y = k^(x) they should look like this: y | | | | | | | | | | | | | | _- | ___-- |---------___________ x As you can see, the line curves upwards, increasing in gradient costantly. It's also interesting to note that all exponential graphs (without a specified y intercept), intersect y at 1 as n^0 === 1 If you draw the gradient graph of an exponential, you get another exponential graph, they are usually slightly different to the original graph, for instance, the gradient graph of 2^x is slightly shallower than 2^x and the gradient graph of 3^x is slightly steeper than 3^x, As you can see, the gradient graph and initial graph must cross at a certain value between 2 and 3 that value is about 2.718, the gradient graph 2.718^x is exactly the same as 2.718^x, we call this value e. Similar to pi, the number e actually goes on forever, I just rounded it to 2.718, the first 10 digits are 2.718281828. So e is a special number because if you differenciate it, you get the same value: ``` y = e^x dy/dx = e^x y = e^kx dy/dx = ke^kx ```