Logarithms and implicit differentiation
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Further derivatives of exponential and logarithmic functions
We use implicit differentiation to find the derivative of [Equation goes here - download the original pdf to see it.] as follows [Equation goes here - download the original pdf to see it.] Example (2) Find the derivative of [symbol] where . What are the coordinates of its stationary point? What kind of stationary point is it? Sketch the curve of [equation]. Solution [Equation goes here - download the original pdf to see it.] To find the character of the stationary point let us see how [Equation goes here - download the original pdf to see it.] changes around [Equation goes here - download the original pdf to see it.] So this is a minimum. The graph of [Equation goes here - download the original pdf to see it.] is asymptotic to the y-axis; that is [Equation goes here - download the original pdf to see it.] Also [Equation goes here - download the original pdf to see it.] [Diagram goes here - download the original pdf to see it.] Example (3) Find the derivative of[Equation goes here - download the original pdf to see it.] where [Equation goes here - download the original pdf to see it.] Solution Example goes here - download the original pdf to see it.] Example (4) Find the derivative of [Equation goes here - download the original pdf to see it.] [Example goes here - download the original pdf to see it.]
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Contents of
Logarithms and implicit differentiation
1 Logarithms and Implicit Differentiation- Prerequisites
2 Further derivatives of exponential and logarithmic functions
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