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Also, which is the instantaneous velocity of the body at time ‘t’.

Example 10

Find the gradient of the curve y = 2 x2 - 6 x at (2 , 4 ) from the first principle.

1) y = f (x) = 2 x2 - 6 x

2) y + D y = f ( x + D x ) = 2 ( x + D x ) 2 - 6 ( x + D x )

Subtracting

D y = 2 x2 + 4 x D x + 2 ( D x )2 - 6 x - 6 D x - 2 x2 + 6 x

= 4 x D x + 2 (D x)2 - 6 D x

3) \

= 4 x + 2 D x - 6

4) \

= ( 4 x + 2 D x - 6 )

= 4 x + 2 ( 0 ) - 6

= 2

\ The gradient at ( 2 , 4 ) is 2.

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Example 11

Differentiate y = Öx w . r. to x, from the first principle.

1) y = Öx

\ y + D y =

2) Subtracting

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