� More rules of differentiation :
f ( x) � sin x � f �( x) � cos x f ( x) � p( q( x)) � f �( x) � p�( q( x)) � q�( x) f ( x) � cos x � f �( x) � � sin x
1 f ( x) � tan x � f �( x)
�
2 cos x f ( x) � e x � f �( x)
� e 1 f ( x) � ln x � f �( x)
� x
x f ( x) � p( x) q( x) � f �( x) � p�( x) q( x) � p( x) q�( x)
px ( ) f( x)
� qx ( ) p�( x) q( x) � p( x) q�( x)
� f�( x) �
2
( qx ( ))
� f��( a) � 0 and f�� ( x) changes sign at x� a: ( a, f ( a )) is a point of inflexion of f( x )
dN dN dx
� � � : Rate of change of N with respect to the time t dt dx dt
� Tests for optimization : 1 . First derivative test 2 . Second derivative test
� Applications in kinematics : 1 . st (): Displacement with respect to the time t 2 . v( t) � s�( t)
: Velocity
3 . a( t) � v�( t) : Acceleration
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Integration and Trapezoidal Rule
� Integrals of a function y � f ( x) :
1 . � f ( x) dx : Indefinite integral of f( x ) b
2 . � f ( x ) d x : Definite integral of f( x ) from a to b a www . seprodstore . com
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