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Math Help - find the derivative of function using

  1. #1
    Junior Member
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    find the derivative of function using

    f(x+h)-f(x)/h

    1) f(x)=5x^3
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  2. #2
    Senior Member apcalculus's Avatar
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    f(x+h) = 5(x+h)^3 = 5(x^3+3x^2h+3xh^2+h^3)

    f(x) = 5x^3


    Compute

    f(x+h) - f(x) = 5x^3 + 15x^2h+15xh^2+5h^3 - 5x^3 = 15x^2h+15xh^2+5h^3

    Don't forget to use the limit notation in your definition:

    \lim_{h\to 0} \frac{f(x+h)-f(x)}{h}=\lim_{h\to 0} \frac{15x^2h+15xh^2+5h^3}{h}=\lim_{h\to 0}15x^2+15xh+5h^2=...

    Good luck!
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