Notes Day 3 - 4.4 Exponential and Logarithmic Derivatives ... · Notes Day 3 4.4 Exponential and...

Notes Day 3 4.4 Exponential and Logarithmic Derivatives.notebook April 16, 2018

Section 4.4 Exponential and Logarithmic Derivatives

When composite functions

are involved the

formulas become


Proof of the Derivative of ex

Problem: Find the derivative of y=e x , using the limit definition for differentiation.

As a result, we can say that the derivative (slope) of y= ex at x = 0 is 1. We can also express this using the definition of the derivative.

If we draw a tangent to the curve at the point (0,1), wefind that its slope is exactly 1.


OR

Ex(1) Find the derivative of each function.


OR



Exercises: Page 183184 # 1 27 odd, 37 41 odd

OR


When the same variable appears in both the base and the exponent we need another approach to finding its derivative.

This approach is called logarithmic differentiation

Differentiate


Ex(2) Use the technique of logarithmic differentiation to find


The technique of logarithmic differentiation can also be used when finding the derivatives of complicated functions involving products, quotiens, or power.

Let's look at this question that was previously done with the

product rule.

Ex(3) Use the technique of logarithmic differentiation to find


Exercises: Page 184 # 43 48 all

Notes Day 3 - 4.4 Exponential and Logarithmic Derivatives ... · Notes Day 3 4.4 Exponential and...

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