The Product and Quotient Rules The Product Rule
Proof: We have
f(x+h) g(x+h) - f(x+h) g(x) +
f(x+h) g(x) - f(x) g(x)
f(x+h) g(x+h) - f(x+h) g(x)
f(x+h) g(x) - f(x) g(x)
g(x+h) - g(x)
f(x+h) - f(x) = [lim f(x+h)] g'(x) + g(x) f '(x) = f(x)g'(x) + g(x)f'(x)
Example Solution:
The Quotient Rule Remember the poem "lo d hi minus hi d lo square the bottom and away you go" This poem is the mnemonic for the taking the derivative of a
quotient.
Solution:
2x + 2 - 2x + 1
3 Exercise Suppose that the cost of producing x snowboards per hour is given by
50x + 1000 find the marginal cost when x = 10
Answer (hold mouse over yellow rectangle for the answer)
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