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Math Help - Derivatives

  1. #1
    Junior Member surffan's Avatar
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    Derivatives

    There are a couple equations I was trying to find the derivative of, if anyone can tell me if these look right.

    1. If f(x)=e^(3x^2+x), find f'(2)
    f'(x) = e^(3x^2+x)(6x)
    f'(2) = e^(3(2)^2+2)(6(2))
    = (1.4)(10^7)
    2. Find the slope of the tangent to the function f(x)=2^(x^2+3x) when x=3
    f'(x) = 2^(x^2+3x)ln2(2x+3)
    f'(3) = 2^(3^2+3(3))ln2(2(3)+3)
    = the number is really large so i dont think this is correct.
    3. Find the derivative of f(x) = sqrt(x)(2x+3)^2
    f'(x) = (x)^(1/2)' (2x+3)^2 + (x)^(1/2)(2x+3)^2'
    f'(x) = ((1/2)x^(-1/2)) ((1)(2x+3)^2) +((x)^(1/2)) ((2)(2x+3)(2))
    f'(x) = (2x+3)^2/ (1/2)x^(1/2) + 4x^1/2(2x+3)
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  2. #2
    MHF Contributor
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    Quote Originally Posted by surffan View Post
    There are a couple equations I was trying to find the derivative of, if anyone can tell me if these look right.

    1. If f(x)=e^(3x^2+x), find f'(2)
    f'(x) = e^(3x^2+x)(6x+1)
    f'(2) = e^(3(2)^2+2)(6(2)+1)=13e^(14)
    = (1.4)(10^7)
    2. Find the slope of the tangent to the function f(x)=2^(x^2+3x) when x=3
    f'(x) = 2^(x^2+3x)ln2(2x+3)
    f'(3) = 2^(3^2+3(3))ln2(2(3)+3)=(9ln2)2^(18)
    = the number is really large so i dont think this is correct.
    The graph is very steep at x=3
    3. Find the derivative of f(x) = sqrt(x)(2x+3)^2
    f'(x) = (x)^(1/2)' (2x+3)^2 + (x)^(1/2)(2x+3)^2'
    f'(x) = ((1/2)x^(-1/2)) ((1)(2x+3)^2) +((x)^(1/2)) ((2)(2x+3)(2))
    f'(x) = (2x+3)^2/ (1/2)x^(-1/2) + 4x^1/2(2x+3)
    Hi surffan,

    just a couple of corrections needed.
    These curves are very steep for the value of x chosen.
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