Textbook Guide Mathematics: Product Rule, Power Rule, Relative Growth Rate
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MAT133Y1 Full Course Notes
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Don"t use the quotient rule every time you see a quotient. Sometimes it"s easier to rewrite a quotient first to put it in a form that is simpler for the purpose of differentiation. Note: in using the chain rule we work from the outside to the inside. Implicit differentiation consists of differentiating both sides of the equation with respect to and then solving the resulting equation for y". If we combine formula 2 with the chain rule: The power rule: in general there are four cases for exponents and bases: 3. 7 rates of change in the natural and social sciences. The derivative can be interpreted as the instantaneous rate of change of y with respect to x. There are multiple applications in the areas of physics, chemistry, biology, economics, and other sciences. Equation 1 is sometimes called the law of natural growth (if k>0) or the law of natural decay (if k<0).
