Find the derivative of the following functions (it is to be understood that a , b , c , d , p , q, r and s are fixed non-zero constants and m and n are integers):
Consider the function,
f ( x ) = 1 + 1 x 1 − 1 x = x + 1 x x − 1 x = x + 1 x − 1
The quotient rule of derivative to find the derivative of the function is,
d d x ( U V ) = ( U V ′ − V U ′ ) V 2
Where U ′ and V ′ are the derivative of their respective functions.
Apply quotient rule of derivative in the given function,
f ′ ( x ) = ( x − 1 ) d d x ( x + 1 ) − ( x + 1 ) d d x ( x − 1 ) ( x − 1 ) 2 = ( x − 1 ) ( 1 ) − ( x + 1 ) ( 1 ) ( x − 1 ) 2 = x − 1 − x − 1 ( x − 1 ) 2 = − 2 ( x − 1 ) 2
Thus, the derivative of 1 + 1 x 1 − 1 x is − 2 ( x − 1 ) 2 .
Consider the function,
The quotient rule of derivative to find the derivative of the function is,
Where
Apply quotient rule of derivative in the given function,
Thus, the derivative of
