Question

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

Answer 1

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.

Answer 2

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. :(