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Introduction to Derivatives

Techniques of Differentiation

Problems for "The Concept of the Derivative"

Techniques of Differentiation, page 2

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Basic Rules

Because the derivative is a limit, many of the rules of limits apply to the derivative:

  1. (cf (x))' = c(f'(x)) where c is a constant. This says that the derivative of a scalar multiple of a function is equal to the derivative of the function multiplied by the scalar multiple.
  2. (f (x) + g(x)) = f'(x) + g'(x) . The derivative of a sum of two functions is equal to the sum of the individual derivatives.

The Power Rule

This is a powerful way of finding the derivative of a polynomial function. It says:

x n = nx n-1    

where n is a real number. For example,

x 4 = 4x 3    

The Product Rule

If f and g are two differentiable functions, then (fg)' = f'g + g'f . For example,

(3x)( = 3 +3x( x - )    

The Quotient Rule

If f and g are two differentiable functions, then

=    

For example,

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