Quoting me
Let f ( x ) = x + 1 2 x − 1 .
Find f ′ ( 4 ) to two decimal places.
The answer is 0.12.
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1 solution
we could also rewrite the function as
f ( x ) = x + 1 2 ( x + 1 ) − 3 = 2 − x + 1 3 ,
then apply the power rule to quickly see that f ′ ( x ) = ( x + 1 ) 2 3 .
Please @Brilliant Staff Rate this Problem To Calculus Level 2.
By quotient rule:
f ′ ( x ) = ( ( x + 1 ) ( 2 x − 1 ) ′ − ( 2 x − 1 ) ( x + 1 ) ′ ) / ( x + 1 ) 2
This simplifies to 3 / ( x + 1 ) 2 = 3/25 = 0.12