SOLUTION: Use the definition of the derivative to find f ′(x) if (a)f(x)=x^2+x (b)f(x)= 1/(x-1)

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Question 1003757: Use the definition of the derivative to find f ′(x) if
(a)f(x)=x^2+x
(b)f(x)= 1/(x-1)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

(a)
f%28x%29=x%5E2%2Bx
f'%28x%29+=+2x%2B1
(b)
f%28x%29=+1%2F%28x-1%29

using the %28f%28x%2Bh%29-f%28x%29%29%2Fh+method:
lim%28+h-%3E0%29%28f%28x%2Bh%29-f%28x%29%29%2Fh++

=lim+h-%3E0%281%2F%28x%2Bh-1%29-1%2F%28x-1%29%29%2Fh+

=lim+h-%3E0

=lim+h-%3E0%28%28x-1%29-%28x%2Bh-1%29%29%2F%28h%28x-1%29%28x%2Bh-1%29%29

=lim+h-%3E0-h%2F%28h%28x-1%29%28x%2Bh-1%29%29

=lim+h-%3E0-1%2F%28x-1%29%5E2

so,
f'%28x%29+=+-1%2F%28x-1%29%5E2