What is the derivative of e 2x?

The derivative of e 2x is 2e 2x. The rule for differentiating an exponential function is that for f (x)=e u, the derivative is f' (x)=u’.e u. u is the function found in the power of the exponential and u’ is the derivative of this function.

What is the derivative of exponential function E X?

Now that we know the derivative of the exponential function is given by f' (x) = a x ln a, the derivative of exponential function e x using the same formula is given by e x ln e = e x (because ln e = 1). Hence the derivative of exponential function e x is the function itself, that is, if f (x) = e x, then f' (x) = e x.

What is the nth derivative of exponential function E X?

Since the first derivative of exponential function e x is e x, therefore if we differentiate it further, the derivative will always be e x. Hence the nth derivative of e x is e x. Is the Derivative of Exponential Function e x the Exponential Function?