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Math Help - Finding the Derivative by Limit Process

  1. #1
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    Finding the Derivative by Limit Process

    I have the function:
    f(x)=5x+6

    I need to "find the derivative by the limit process".

    Using:
    (f(x+deltax)-f(x))/deltax

    My work:
    (5(x+deltax)+6-(5x+6))/deltax

    (5x+5deltax+6-(5x+6))/deltax

    The two 5x's go away, the 5Δx and Δx go away, so I'm left with 12, which isn't the answer.

    I'm lost.
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  2. #2
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     =\lim_{h\to 0 }\frac{f(x+h)-f(x)}{h}

     =\lim_{h\to 0 }\frac{5(x+h)+6-(5x+6)}{h}

     =\lim_{h\to 0 }\frac{5x+5h+6-5x-6}{h}

     =\lim_{h\to 0 }\frac{5h}{h}

     =\lim_{h\to 0 }5

     =5
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  3. #3
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    Thanks a lot. I need to start using h instead of Δx, since Δx is pretty confusing.
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  4. #4
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    I agree with this.
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  5. #5
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    New question...


    There's just way too many things on my paper and I'm just lost now .
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  6. #6
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    This one will take some doing, here's the first bit, now gettting expanding!

    =\lim_{h\to 0 }\frac{\left(9(x+h)^2-3(x+h)-\frac{3}{(x+h)^2}\right)-\left(9x^2-3x-\frac{3}{x^2}\right)}{h}
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