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3.2 Rules of Differentiation
Theorem 3.2: The Constant Rule.
If
is a constant function then
Examples Find the derivative f '(x)
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Theorem 3.3: The Power Rule.
If
is a power function where n>0 integer then
Example: The Power Rule.
Find the derivatives:
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Theorem 3.3: The Power Rule.
If
is a power function where n>0 integer then
Proof:
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Theorem 3.4: The Constant Multiple Rule.
Consider a constant multiple function:
Example: Constant Multiple and Power Rules.
Find the derivatives:
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Theorem 3.4: The Constant Multiple Rule.
Consider a constant multiple function:
Proof:
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Theorem 3.5: The Sum Rule.
If f(x) and g(x) are differentiable functions then:
Example: Constant Multiple, Power Rule and Sum Rule.
Find the derivatives:
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Theorem 3.5: The Sum Rule.
If f(x) and g(x) are differentiable functions then:
Proof: Let F(x) = f(x)+g(x)
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Higher-Ordered Derivative: Assuming f(x) can be differentiated as
often as possible, the second derivative is given by:
And, the nth derivative is given by:
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