In general, an exponential function is of the form
f(x) = ax where a is a positive constant.
Derivative of the Natural Exponential Function
The exponential function f(x) = ex has the property that it is its own derivative. This means that the slope of a tangent line to the curve y = ex at any point is equal to the y-coordinate of the point.
We can combine the above formula with the chain rule to get
Differentiate the function y = e sin x
Differentiate the function y = e–3xsin4x
Using the Product Rule and the above formulas, we get
Derivative of ax
Derivative of ag(x)
Differentiate y = x3 + 3x
Differentiate y = 52x+1
Derivatives of Exponential Functions
The derivative of an exponential function can be derived using the definition of the derivative. Derivatives of exponential functions involve the natural logarithm function, which itself is an important limit in Calculus, as well as the initial exponential function. The derivative is the natural logarithm of the base times the original function.
Derivatives of Exponential Functions with Base e
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.