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 √(1-2(x+h)) - √(1-2x)
can be "rationalized" by multiplying top and bottom by √(1-2(x+h)) + √(1-2x).
That way the 0/0 is avoided, and you then have a nonzero factor in the denominator.
Find the requested derivative using limits
a. 𝑓′(-4)if f(x)=sqrt(1-2x)
b. 𝑓′(a)if f(x)=(2x+1)/(x+3)
c. 𝑓′(x) if f(x)=x^-2
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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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