Solving a Derivative Problem with f(x) = SQRT(1-3x)

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The discussion focuses on finding the derivative of the function f(x) = SQRT(1-3x) using the limit definition of a derivative. The calculation involves applying the limit as h approaches zero to derive the expression for f'(x). The final result is f'(x) = -3/(2f(x)), highlighting the relationship between the derivative and the original function. The conversation emphasizes the importance of mastering fundamental derivative concepts for tackling more complex problems in the future. Persistence in practicing algebra is encouraged to build confidence and proficiency.
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My algebra continues to let me down…

How about this one…I know there a simpler ways to do these problems but at this point I’m supposed to do it the hard way.

Using the definition of derivate find f ` (x)

f(x) = SQRT(1-3x)

f ` (x) = lim h->0 [(f(x+h)) – (f(x))]/h

= lim->0 [(SQRT(1-3(x+h))) – (SQRT(1-3x))]/h

= lim->0 [[(SQRT(1-3(x+h))) – (SQRT(1-3x))]/h] . [[((SQRT(1-3x-3h))) + (SQRT (1-3x))]/ [((SQRT(1-3x-3h))) + (SQRT (1-3x))]]

=lim->0 (1-3x-3h-1+3x)/(h[(SQRT(1-3x-3h)) + (SQRT (1-3x))]

= lim->0 -3/[SQRT(1-3x-3h) + SQRT (1-3x)]

= -3/(2(SQRT(1-3x))
 
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Why are you let down by the correct answer? :smile:
 
)

= -3/(2f(x))

So, the derivative of f(x) is -3/(2f(x)).

I understand that this may seem like a difficult and tedious process, but it is important to understand the fundamentals of derivatives in order to solve more complex problems in the future. Keep practicing and don't get discouraged, algebra can be challenging but with persistence and effort, you will improve and become more confident in solving these types of problems. Good luck!
 
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