SOLUTION: Using Limits to Calculate a Derivative Use the definition of the derivative to find f ′(x) if f(x)=x^2+x

Algebra ->  Equations -> SOLUTION: Using Limits to Calculate a Derivative Use the definition of the derivative to find f ′(x) if f(x)=x^2+x      Log On


   

Question 1010142: Using Limits to Calculate a Derivative
Use the definition of the derivative to find f ′(x) if
f(x)=x^2+x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E2+%2B+x

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f%28x%2Bh%29+=+%28x%2Bh%29%5E2+%2B+%28x%2Bh%29

f%28x%2Bh%29+=+x%5E2%2B2xh%2Bh%5E2+%2B+x%2Bh

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%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28x%5E2%2B2xh%2Bh%5E2+%2B+x%2Bh-x%5E2+-+x%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%282xh%2Bh%5E2+%2Bh%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+%28h%282x%2Bh+%2B1%29%29%2Fh

%28f%28x%2Bh%29-f%28x%29%29%2Fh+=+2x%2Bh%2B1

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The difference quotient is %28f%28x%2Bh%29-f%28x%29%29%2Fh+=+2x%2Bh%2B1

If you were to apply the limit as h goes to 0, then 2x%2Bh%2B1 becomes 2x%2B0%2B1+=+2x%2B1

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The derivative f ' (x) is 2x%2B1