Derivatives of Exponential Functions (Cambridge (CIE) A Level Maths) : Revision Note
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Derivatives of Exponential Functions
What is the derivative of e?
y = ex has the particular property
ie for every real number x, the gradient of y = ex is also equal to ex (see Derivatives of Exponential Functions)


e ≈ 2.718 (see "e")
Recall that the derivative is the gradient function for a curve (see First Principles Differentiation)
Graphs and derivatives related to e

The derivative of y = ekx is
The derivative of y = e-kx is
Examiner Tips and Tricks
Remember that (like π) e is a number.
Exam questions can ask for answers to be given as exact values in terms of e (see the Worked Example below).
Worked Example





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