Question

Find the requested derivative using limits

a. ๐‘“โ€ฒ(-4)if f(x)=sqrt(1-2x)

b. ๐‘“โ€ฒ(a)if f(x)=(2x+1)/(x+3)

c. ๐‘“โ€ฒ(x) if f(x)=x^-2

Answers

Steve
These are a bit tedious, but not hard. I'm sure your book has examples just like them. Give it a go, and come back if you get stuck. Show what you did.

Just recall that โˆš(1-2(x+h)) - โˆš(1-2x)
can be "rationalized" by multiplying top and bottom by โˆš(1-2(x+h)) + โˆš(1-2x).

That way the 0/0 is avoided, and you then have a nonzero factor in the denominator.
TayB
Steve I agree they are tedious doing it this way its easier using the derivative rules but even though i know them we arent allowed to use them until the class learns them. :(

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