Derivative Rules - ] = f(x)g'(x) + g(x)f'(x) The Quotient...

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Derivative Rules: The Constant Rule The derivative of a constant function is 0. That is, if c is a real number, then d/dx[ c ] = 0. The Sum and Difference Rules The sum(or difference) of two differentiable functions is differentiable and is the sum(or difference) of their derivatives. d/dx[ f(x) + g(x) ] = f'(x) + g'(x) d/dx[ f(x) - g(x) ] = f'(x) - g'(x) The Constant Multiple Rule If f is a differentiable function and c is a real number, then cf is also differentiable and d/ dx[ cf(x) ] = cf'(x) The Power Rule If n is a rational number, then the function f(x) = x n is differentiable and d/dx[ x n ] = nx n-1 The Product Rule The product of two differentiable functions, f and g , is itself differentiable. Moreover, the derivative of fg is the first function times the derivative of the second, plus the second function times the derivative of the first. d/dx[ f(x)g(x)
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Unformatted text preview: ] = f(x)g'(x) + g(x)f'(x) The Quotient Rule The quotient f/g , of two differentiable functions, f and g , is itself differentiable at all values of x for which g(x) does not = 0. Moreover, the derivative of f/g is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator divided by the square of the denominator. d/dx[ f(x)/g(x) ] = (g(x)f'(x) - f(x)g'(x)) / [g(x)] 2 g(x) does not = 0 The Chain Rule If y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x , then y = f(g(x)) is a differentiable function of x and d/dx[ f(g(x)) ] = f'(g(x))g'(x) The General Power Rule If y = [ u(x) ] n , where u is a differentiable function of x and n is a rational number, then d/dx = [ u n ] = nu n-1 u' ....
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This note was uploaded on 04/10/2008 for the course MATH 132 taught by Professor Julies during the Fall '08 term at Michigan State University.

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