Derivatives of Exponential Functions (Cambridge (CIE) A Level Maths): Revision Note

Derivatives of Exponential Functions

What is the derivative of e?

• y = e^x has the particular property

• ie for every real number x, the gradient of y = e^x is also equal to e^x (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 = e^kx is

  • 

• The derivative of y = e^-kx is

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