Common Calculus Mistakes
Product Rule: Constants

Some problems provide the opportunity for more than one mistake.

The Goal



The Mistakes

Find the mistakes:



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A Correct Solution


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Differentiating the second factor has caused problems here. In the first mistake for some reason the derivative of the second factor was computed to be -2, with the π in the denominator completely ignored. In the second mistake the quotient rule was applied incorrectly (and without need - if the denominator is a constant, pull it out using the constant mutiple rule and differentiate the numerator); parentheses should have been used around the -2 in the numerator, which should therefore have been π(-2) - 0.

The derivative in this example might be more easily handled by using the constant multiple rule to pull the 1/π out in front and multiplying out x(400 - 2x) before differentiating, as follows:


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