2.2 Techniques of Differentiation

2.2 Techniques of Differentiation - 2....

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2.2 Techniques of Differentiation Constant Rule:   For any constant  c , [ ] d c dx = 0 ; the derivative of a constant is zero.   Power Rule:   For any real number  n n n d x nx dx -  = 1 .   Constant Multiple Rule:  If  c  is a constant and  f(x)   is differentiable, then so is  cf(x)  and         ( 29 ( 29 d d cf x c f x dx dx = ; the derivative of a multiple is the multiple of the derivative.   Sum Rule:   If  f(x)  and  g(x)   are differentiable, then so is the sum  S(x) = f(x) + g(x)  and  S’(x) = f ’(x) + g’(x)        ( 29 ( 29 ( 29 ( 29 d d d f x g x f x g x dx dx dx + = + ; the derivative of the sum is the sum of the derivatives.   Relative and Percentage Rates of Change  of a quantity  Q(x)   with respect to  x  is         ( 29 ( 29 ' / ( ) relative rate of

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