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
Example:
Differentiate the function y = e sin x
Solution:
Example:
Differentiate the function y = e–3xsin4x
Solution:
Using the Product Rule and the above formulas, we get
Derivative of ax
Derivative of ag(x)
Example:
Differentiate y = x3 + 3x
Solution:
Example:
Differentiate y = 52x+1
Solution:
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.