(c * f(x))" = c * f "(x)The derivative that a constant times a function is the continuous times the derivative that the function.

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(f(x) ± g(x))" = f "(x) ± g"(x)The derivative the a sum (difference) is the amount (difference ) the the derivatives.
(f(x)g(x))" = f(x)g"(x) + f "(x)g(x)The derivative the a product is the first factor times the derivative the the second plus the second factor times the derivative the the first.
(f(x)/g(x))" = (g(x)f "(x)-f(x)g"(x))/(g(x))²The derivative the a quotient is the bottom time the derivative the the peak minus the top times the derivative of the bottom, everywhere the bottom squared.Lo D(Hi) -Hi D(lo) end the square of what"s below.
(f(g(x))" = f "(g(x) * g"(x)The derivative of a composite function is the derivative of the outside function times the derivative that the within function.
A an approach for recognize the derivatives the implicitly characterized functions. Take the derivative of each term. Treat every y-terms as attributes of x and also multiply dy/dx by every derivatives the y-terms.

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A an approach for discover the derivatives of complicated products and also quotients through powers or attributes with variables increased to variable powers. Take the natural log (ln) the both sides of the equation and use log rules come simplify. Then take the derivative. Remember come exponentiate both political parties to obtain your last answer.
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Applied Partial Differential Equations v Fourier collection and Boundary value Problems5th EditionRichard Haberman
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Differential Equations v Boundary-Value Problems, international Metric Edition9th EditionDennis G. Zill
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