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Example 37

Find y’ at the point (1, 0) if xy = log (xy)

Solution :  xy = log (xy). Differentiating w. r. to. x

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Example 38

If xp yp = ( x + y)p+q Find

Solution :  xp yp = ( x + y)p+q

Note that here we will use the technique of logarithmic differentiation. i.e. Taking logs of both the sides, we get

p log x + q log y = (p + q) log (x + y)

Differentiating w. r. to x. we get

Index

4. 1 Derivability At A Point
4. 2 Derivability In An Interval
4. 3 Derivability And Continuity Of A Function At A Point
4. 4 Some Counter Examples
4. 5 Interpretation Of Derivatives
4. 6 Theorems On Derivatives (differentiation Rules)
4. 7 Derivatives Of Standard Functions
4. 8 Derivative Of A Composite Function
4. 9 Differentiation Of Implicit Functions
4.10 Derivative Of An Inverse Function
4.11 Derivatives Of Inverse Trigonometric Functions
4.12 Derivatives Of Exponential & Logarithmic Functions
4.13 Logarithmic Differentiation
4.14 Derivatives Of Functions In Parametric Form
4.15 Higher order Derivatives

Chapter 5