lect116_8rev_f11

lect116_8rev_f11 - Tuesday, September 27 Lecture 8 :...

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Tuesday, September 27 Lecture 8 : Differentiation: Rules (Refers to section 3.5 in your text) Students who have mastered the content of this lecture know about : The differentiation formulas: derivatives of sums, products, scalar products, quotients and the power rule. Students who have practiced the techniques presented in this lecture will be able to : Find the derivative of simple functions using the above differentiation formulas. The following five differentiation formulas are important. The proof of the first four follows directly from the definition of the derivative. 8.1 Theorem – Differentiation formulas for simple functions: a) For any constant c , the derivative of f ( x ) = c is b) For the function f ( x ) = x c) Scaling rule : If c is a constant and f ( x ) is any function, d) Sum rule : If f ( x ) and g ( x ) are both differentiable on an interval ( a , b ) then is any function, e) Power rule : If n is a non-zero number and f ( x ) = x n
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Proof: a) b) c) d) e) We will provide an easy proof of the power rule once we have learned logarithmic differentiation.
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lect116_8rev_f11 - Tuesday, September 27 Lecture 8 :...

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