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Math Help - Derivation and equations

  1. #1
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    Arrow Derivation and equations

    Hi !

    I have two problems concerning computing the derivative and solving the equations. Just so the figures are correct I copied the problems from my PDF document and attached as word documentation with this message.

    I hope that someone can help me !
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  2. #2
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    Quote Originally Posted by Vilkku View Post
    Hi !

    I have two problems concerning computing the derivative and solving the equations. ...
    Hello, Vilkku,

    a) f'(x) = 12x + 4x^(-3)

    b) Use quotient rule:
    Code:
             (3x-1)*1 - (x+2)*3       -7
    f'(x) = ------------------- =  -----------
                  (3x-1)            (3x-1)
    c) Use product rule and chain rule

    f'(x) = e^(3x)*2x + x*e^(3x) * 3 = x*e^(3x)(2 + 3x)

    d) Use chain rule:

    f'(x) = 4(5x - x) * (15x - 1)

    Solve the equations:

    a) e^(2x-1) = 3 <==> 2x-1 = ln(3) <==> x = (1 + ln(3))

    b) 2^x - 15 = 0 <==> e^(x*ln(2)) = 15 <==> x*ln(2) = ln(15) <==> x = (ln(15))/(ln(2))

    c) 50*1.05^(x) = 70 <==> e^(x*ln(1.05)) = 7/5 <==> x = (ln(7/5))/(ln(1.05))

    EB
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