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Example 67

If x = a sec q , y = a tan q , Find at q =

Solution: x = a sec q

       = a sec q tan q

          and y = a tan q

       = a sec2 q then,

             =

         =

         =

   =

          =

          =

          =

Example 68

If x = a ( q - sin q ) and y = a ( 1 - cos q ). Show that


Solution : x = a ( q - sin q )

    = a ( 1 - cos q )

=

           and y = a (1 - cos q)

    = a (sin q)

=

    =

=

=

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





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