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Easy: Product of two binomials
Product rule: (fg)′ = f′g + fg′, the derivative of the first times the second plus the first times the derivative of the second. Quotient rule: (f/g)′ = (f′g − fg′)/g², low d-high minus high d-low, over the denominator squared. The order matters in the quotient rule because of the subtraction.
Find the derivative. Simplify.
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No. (fg)′ = f′g + fg′. For x²·sin x, the derivative is 2x sin x + x² cos x, not 2x cos x.
"Low d-high minus high d-low, over low squared": (f/g)′ = (g·f′ − f·g′)/g². The subtraction makes the order matter.
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