Copy_of_3.9b_notes

# Copy_of_3.9b_notes - 3.9b More on Derivatives of...

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Calculus Section 3.9b Page51 3.9b More on Derivatives of Exponential and Logarithmic Functions Yesterday you learned several new formulas e x ( ) = e u ( ) = ln x ( ) = ln u ( ) = The natural logarithm function obeys all of the laws of logarithms that you learned in Mathematics 12. ln x = y ln1 = ln e = ln e x = e ln x = ln ab = ln a b = ln a n = log b a = Logarithmic Differentiation (technique of taking the ln of both sides then differentiating implicitly) Example 1 Find the derivative of y = x x Example 2 Find the derivative of y = 3 x

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Page 52 We now have a new “short-cut” formula for taking the derivative of a function in the form y = a x where a is a constant. a x ( ) = a u ( ) = Example 3 Using the Algebra of logarithms At what point on the graph of the function y = 2 x - 3 does the tangent line have slope 21? Derivative of y = log a x Change to exponential form and differentiate implicitly. y
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Copy_of_3.9b_notes - 3.9b More on Derivatives of...

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