CIE A Level Maths: Pure 3復習筆記2.1.4 Derivatives of Exponential Functions
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
Exam Tip
- 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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