Find the derivative of the functions by using the Quotient Rule. Simplify your answer. 1. f(x)=(x+1)/(x-1) 2. f(x)=(x^2-3x+4)/(x+2) 3. (sqrt(x)-6)/(sqrt(x)+6)

Glenn Hopkins 2022-07-16 Answered
Find the derivative of the functions by using the Quotient Rule. Simplify your answer.
1. f ( x ) = x + 1 x 1
2. f ( x ) = x 2 3 x + 4 x + 2
3. x 6 x + 6
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Answers (1)

phravincegrln2
Answered 2022-07-17 Author has 19 answers
1. f ( x ) = x + 1 x 1
Using the Quotient rule
f ( x ) = ( x 1 ) d d x ( x + 1 ) ( x + 1 ) d d x ( x 1 ) ( x 1 ) 2 = ( x 1 ) x 1 ( x 1 ) 2 f ( x ) = 2 ( x 1 ) 2
2. f ( x ) = x 2 3 x + 4 x + 2 f ( x ) = ( x + 2 ) d d x ( x 2 3 x + 4 ) ( x 2 3 x + 4 ) d d x ( x + 2 ) ( x + 2 ) 2 f ( x ) = ( x + 2 ) ( 2 x 3 ) ( x 2 3 x + 4 ) ( x + 2 ) 2 f ( x ) = 2 x 2 3 x + 4 x 6 x 2 + 3 x 4 ( x + 2 ) 2 f ( x ) = x 2 + 4 x 10 ( x + 2 ) 2
3. x 6 x + 6 d d x [ x 6 x + 6 ] = ( x + 6 ) d d x ( x 6 ) ( x 6 ) d d x ( x + 6 ) ( x + 6 ) 2 ( x + 6 ) 1 x 2 ( x 6 ) 1 x 2 ( x + 6 ) 2 = 6 x ( x + 6 ) 2

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