Task 3: Gradient function of exponential functions

Explore the algebraic form of the gradient function of exponential functions and meet THE exponential function, .
Adjust the value of a using the slider. 1. What is the general form of the derivative of ? 2. What do you notice about the function/graph and its derivative/gradient for the special value of found in Task 2? The special value is called "". 3. Use your calculator to find the value of to 3 decimal places. is an exponential function. is THE exponential function. Type "f(x)=e^x" into the input box, selecting "e" from the drop-down menu to the right of the box. 4. Write down the derivative of . 5. Hence write down the integral of .