Logarithmic Differentiation
Logarithmic Differentiation
Lesson objective followed by...
0:36 Functions We Know How to Differentiate
3:38 A Function That Requires Logarithmic Differentiation
5:57 Main Steps for Logarithmic Differentiation
6:12 Ex. 1) y = x^(sin x)
6:20 Take the Natural Log of Both Sides
6:26 Use the Power Property of Logarithms
6:40 Take d/dx of Both Sides
6:50 Use Implicit Differentiation on the Left Side & the Product Rule on the Right Side
8:56 Isolate dy/dx
9:25 Replace y With its Rule
10:12 Ex. 2) f(x) = (x^3 + 4)^(cos x)
10:34 Take the Natural Log of Both Sides
10:49 Use the Power Property of Logarithms
11:16 Take d/dx of Both Sides
11:31 Use Implicit Differentiation on the Left Side & the Product Rule on the Right Side
13:47 Isolate f ' (x)
14:10 Replace f(x) With its Rule
Logarithmic Differentiation is Optional for Example 3
14:26 Ex. 3) f(x) = [ (3x + 7)^5 ] / [ (x+2) ^ (1/3) ]
15:41 Take the Natural Log of Both Sides
15:51 Use the Properties of Logarithms to Expand the Right Side of the Equation
18:22 Take d/dx of Both Sides
18:30 Use Implicit Differentiation on the Left Side & Differentiate the Right Side Using the Chain Rule
20:42 Isolate f ' (x)
21:10 Replace f(x) With its Rule
21:38 Summary of Lesson
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