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Math Help - Differentiate?

  1. #1
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    Are my differentiate answers right?

    1.Equation: f(x)=3ln(3-7x)
    Solution: [tex]f'(x)=(3*-7)*\frac{u'}{u}
    = f'(x)=\frac{-21}{2-7x}

    2.Equation: f(x)=e^{5x+2}
    solution: f'(x)=5e^{5x+2}

    3. Equation: g(x)=7^{x-3}+25
    Solution: g'(x)=7^{x-3}Log7

    4. Equation: f(x)=Log3x-Ln3
    Solution: f'(x)=\frac{1}{x Log3}

    5. Equation: h(x)=log2(5x+4)
    Solution: h'(x)=\frac{5}{(5x+4)(log2)}

    6. Equation: y= Ln \frac{(x-2)^4}{(1+x)^5}
    Solution: Unsure of how to solve

    Derivative of

    1. Equation= a^x
    Solution=???

    2 Equation= e^u
    Solution= a^u*u^1 = u^1*e^x or is it e^u

    3 Equation = a^u
    solution = ???

    4. Find Result
    Equation Ln*\frac{u^4*}{z^6}
    Solution = \frac{1}{x}*\frac{(u^4*v)(6z^5)-(4u^5)(z^6)}{(z^6)^2}
    Last edited by MathKidd; March 29th 2010 at 12:14 AM.
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by MathKidd View Post
    Is differentiate the same as derivatives? and is this question correct?

    Problem: f(x)=e Raised to the power of or ^ (5x+2)
    Solution: = 5e Raised to the power of or ^ (5x+2)
    or would it be written as f1(x)=5e Raised to the power of or ^ (5x+2) (Assuming differentiate and derivatives are the same.)
    Yes differentiate is the same as finding the derivative, Now to your question:

    f(x)=e^{5x+2}. Your latex input seems incorrect, but I guess this is what you are asking.

    so,

    f'(x) = 5 \times e^{5x+2}

    and we come to the conclusion that your answer is correct!
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  3. #3
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    Ok...
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  4. #4
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    a^x= e^{ln a^x}= e^{x ln a}.

    Therefore, (a^x)'= e^{x ln a}(ln x)= a^x ln a.

    Notice that e^x is "special" only because ln e= 1.
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  5. #5
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    are my other solutions valid?
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  6. #6
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    Quote Originally Posted by MathKidd View Post
    6. Equation: y= Ln \frac{(x-2)^4}{(1+x)^5}
    Solution: Unsure of how to solve
    y= ln \frac{(x-2)^4}{(1+x)^5}

    =4ln(x-2)-5ln(1+x)

    Now can you find the derivative?

    Quote Originally Posted by MathKidd View Post
    4. Find Result
    Equation Ln\frac{u^4*}{z^6}
    Solution = \frac{1}{x}*\frac{(u^4*v)(6z^5)-(4u^5)(z^6)}{(z^6)^2}
    This is like #6 above

    Quote Originally Posted by MathKidd View Post
    5. Equation: h(x)=log2(5x+4)
    Solution: h'(x)=\frac{5}{(5x+4)(log2)}
    h(x)=log_2(5x+4)

    h'(x)=\frac{5}{(5x+4)(ln2)}
    Last edited by ione; March 29th 2010 at 07:56 AM.
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