Deriving the Differentiation Rule for an Exponential Function with Base b and Examples
Deriving the Differentiation Rule for an Exponential Function with Base b and Examples
Lesson objectives followed by...
1:53 f(x)=ln x and g(x)=e^x are Inverse Functions
3:56 Writing f(x)=b^x in Terms of the Base e
6:21 Finding the Derivative of f(x)=b^x Using f Written in Terms of the Base e
9:20 The Differentiation Rule for f(x)=b^x
Finding Derivatives of Functions
9:36 Ex. 1) y= (x^4)*(7^x)
10:32 Using the Product Rule
11:33 Simplifying the Answer
12:37 Ex. 2) y=5 ln (e^4x)
13:02 Simplifying Before Differentiating
15:19 Differentiating
15:32 Ex. 3) y=2e^(sin x)
15:54 Using the Chain Rule
17:06 Summary of the Lesson
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