4.3 – Differentiation of Exponential and Logarithmic Functions Math 140 4.3 – Differentiation of Exponential and Logarithmic Functions

𝒅 𝒅𝒙 𝒆 𝒙 = 𝒆 𝒙 𝒅 𝒅𝒙 𝐥𝐧 𝒙 = 𝟏 𝒙 𝒅 𝒅𝒙 𝒃 𝒙 = 𝒃 𝒙 𝐥𝐧 𝒃 𝒅 𝒅𝒙 𝐥𝐨𝐠 𝒃 𝒙 = 𝟏 𝒙 𝐥𝐧 𝒃 What does that mean?

Ex 1. Differentiate: 𝑓 𝑥 = 𝑥 3 𝑒 𝑥 𝑓 𝑥 = 𝑒 𝑥 2 +1 𝑓 𝑥 = ln 𝑥 3 𝑥 𝑓 𝑥 = ln 2 𝑥 2 +1 𝑓 𝑥 = 3 5𝑥+2

________________________ is a technique to help differentiate functions with many products, quotients, and powers. Ex 2. Use logarithmic differentiation to find the derivative of the following function. 𝑓 𝑥 = 4 𝑥+2 1−2𝑥 3

Logarithmic differentiation ________________________ is a technique to help differentiate functions with many products, quotients, and powers. Ex 2. Use logarithmic differentiation to find the derivative of the following function. 𝑓 𝑥 = 4 𝑥+2 1−2𝑥 3

Logarithmic differentiation ________________________ is a technique to help differentiate functions with many products, quotients, and powers. Ex 2. Use logarithmic differentiation to find the derivative of the following function. 𝑓 𝑥 = 4 𝑥+2 1−2𝑥 3