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Product and Quotient Rules and Higher Order Derivatives
Section 2.3 AP Calc
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Thm 2.7 The Product Rule The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of is the first function times the derivative of the second, plus the second function times the derivative of the first.
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For products with more than 2 factors:
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Thm 2.8 The Quotient Rule The quotient of two differentiable functions f and g is itself differentiable at all values of x for which . Moreover, the derivative of is given by:
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Thm 2.9 Derivatives of Trig Functions
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Use the Quotient Rule to prove
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Find the derivative:
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Characteristics of simplified derivatives:
-Absence of negative exponents -Combining of like terms
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s(t) v(t)=s’(t) a(t)=v’(t)=s’’(t)
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Higher Order Derivatives:
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Find the Second Derivative of
Find the 2nd Derivative:
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