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Math Help - Derivative Question

  1. #1
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    Derivative Question

    I have started reviewing derivative in class and have a few questions.

    First off I am wondering if I have calculated the derivatives for the following correctly.

    1) f(t) = 2 - (2/3)t
    f'(t) = -2/3
    2)f(x) = (√x^5)- 3x^-7
    f'(t) = (√5x^4) - 21x^-8

    My second question is there is a derivative rule for the sum which states "The derivative of a sum is the sum of the derivatives".

    Is there a rule that applies the same way for the difference? Which would state the derivative of a difference is the difference of the derivatives?

    Thanks for any help
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  2. #2
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    Your derivative for # 2 is wrong.
     f(x)=x^{5/2}-3x^{-7}
    You would use the power rule and the chain rule for this problem if you were to leave  \sqrt {x^5}
     f'(x)= \frac {5} {2} x^{3/2} + 21x^{-8}

    There is a rule that states "if f and g are differentiable at x, then so are f+g and f-g" and
     \frac {d} {dx} [f(x)-g(x)]=\frac {d} {dx} [f(x)]-\frac {d} {dx} [g(x)]
     \frac {d} {dx} [f(x)+g(x)]=\frac {d} {dx} [f(x)]+\frac {d} {dx} [g(x)]
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  3. #3
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    One more quick question. If I am given the functions

    f(x) = 5sin(s) - 6s^3cos(s)

    Do i use the product rule for the 6s^3cos(s) part of the equation then with that result do I use the difference rule for the whole equation of f(x)?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by fishguts View Post
    One more quick question. If I am given the functions

    f(x) = 5sin(s) - 6s^3cos(s)

    Do i use the product rule for the 6s^3cos(s) part of the equation then with that result do I use the difference rule for the whole equation of f(x)?
    Exactly...but be careful...

    You use the difference rule, but for the 6s^3\cos(s) term, you would need to apply the product rule.

    ...and I think its f(s), not f(x)

    So it would be f'(s)=\frac{\,d}{\,ds}\left[5\sin(s)\right]-\frac{\,d}{\,ds}\left[6s^3\cos(s)\right]

    --Chris
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