For example, f(x)=x^2+x.... I don't understand how to do this when it does give you the x.... Thanks for the help!
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f(x) = x² + x
f(x+h) = (x+h)² + (x+h) = x²+2hx+h² + x+h
f(x+h) - f(x)
f '(x) = lim ———————
h→0 h
(x²+2hx+h² + x+h) - (x² + x)
f '(x) = lim ——————————————
h→0 h
x²+2hx+h² + x+h - x² - x
= lim ——————————————
h→0 h
2hx+h²+h
= lim ————————
h→0 h
h(2x+h+1)
= lim ————————
h→0 h
= lim (2x+h+1) = 2x+0+1 = 2x + 1 ← ANSWER
h→0
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f(x) = x² + x
f(x+h) = (x+h)² + (x+h) = x²+2hx+h² + x+h
f(x+h) - f(x)
f '(x) = lim ———————
h→0 h
(x²+2hx+h² + x+h) - (x² + x)
f '(x) = lim ——————————————
h→0 h
x²+2hx+h² + x+h - x² - x
= lim ——————————————
h→0 h
2hx+h²+h
= lim ————————
h→0 h
h(2x+h+1)
= lim ————————
h→0 h
= lim (2x+h+1) = 2x+0+1 = 2x + 1 ← ANSWER
h→0
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Can you rephrase that question, or explain what you're really trying to do, at least with the f^1(x) part?