Find f'(x) if f(x)=sqrt(9-x) and state its domains of f'(x) =lim_(h -> 0) (f(x+h)-f(x))/(h) =lim_{h -> 0) (sqrt(9-(x+h))-sqrt(9-x))/(h) ((sqrt(9-(x+h))+sqrt(9-x))/(sqrt(9-(x+h))+sqrt(9-x)))

Ciara Rose 2022-07-16 Answered
Find f'(x) if f ( x ) = 9 x and state its domains of f'(x)
= lim h 0 f ( x + h ) f ( x ) h = lim h 0 9 ( x + h ) 9 x h ( 9 ( x + h ) + 9 x 9 ( x + h ) + 9 x )
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Answers (1)

kitskjeja
Answered 2022-07-17 Author has 13 answers
Given f ( x ) = 9 x f ( x ) = lim h 0 f ( x + h ) f ( x ) h = lim h 0 9 ( x + h ) 9 x h = lim h 0 9 x h 9 x h × 9 x h + 9 x 9 x h + 9 x = lim h 0 ( 9 x h ) 2 ( 9 x ) 2 h ( 9 x h + 9 x ) = lim h 0 9 x h ( 9 x ) h ( 9 x h + 9 x ) = lim h 0 h h ( 9 x h + 9 x ) = lim h 0 1 9 x h + 9 x = 1 9 x 0 + 9 x = 1 9 x + 9 x = 1 2 9 x f ( x ) = 1 2 9 x ,  it is defired if  9 x > 0 , 9 > x , x < 9.
x ( , 9 )
demain of f'(x) is ( , 9 )

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