Product and fraction of functions.1. The derivative of a constant is
1. The derivative of sum (difference) of two functions equals the sum (difference) of the derivatives of functions: (u±v)¢= u¢±v¢. 3. The constant factor can be factored outside the sign of the derivative (k·u)¢= k(u)¢. 4. The derivative of the product of two functions equals the derivative of the first function, multiplied by the second, plus the derivative of the second, multiplied by the first, i.e., (u· v)¢= u¢v+uv¢. (2)
Example. Find the derivative:
5. The derivative of fraction is defined by the following formula
Example.
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