Derivatives of Exponential Functions (Edexcel IAL Maths)

Spec point — 4.1

Derivatives of exponential functions

What is the derivative of e^x?

• y = e^x has the particular property that

$\frac{dy}{dx}=e^{x}$

• i.e. 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)

What is the derivative of y = e^kx and y=e-^kx?

• The derivative of y = e^kx is

• $\frac{dy}{dx}=ke^{kx}$

• The derivative of y = e^-kx is

  • $\frac{dy}{dx}=-ke^{-kx}$

Exam Hint

• 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