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Math Help - Differentiation Problems

  1. #1
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    Differentiation Problems

    Hi,

    I am in my late 20's and am going for an interview next week where I am required to do a maths test (arrgghh!) I havent done maths now in nearly 10 years but I was quite good at the time, but Im after forgetting all the principles now. I was wondering if you could give me some help on answering the questions below please - Id really appreciate it.

    Differentiate the following:

    f(x) = (x/x+1) 2(squared)

    f(x) = -x +xlnx

    f(x) = xe to the power of 2x + 10x
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  2. #2
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    Quote Originally Posted by tangehayes View Post
    ...

    Differentiate the following:

    1) f(x) = (x/x+1) 2(squared)

    2) f(x) = -x +xlnx

    3) f(x) = xe to the power of 2x + 10x
    to #1):
    Use the chain rule with the quotient rule:

    f(x)=\left(\dfrac{x}{x+1}\right)^2~\implies~f'(x)=  2 \dfrac{x}{x+1} \cdot \dfrac{(x+1) \cdot 1 - x \cdot 1}{(x+1)^2} = \dfrac{2x}{(x+1)^3}


    to #2):
    Use the product rule:

    f(x)=-x+x\cdot \ln(x)~\implies~ f'(x)=-1+\ln(x) \cdot 1+x\cdot \dfrac1x =\ln(x)


    to #3):
    Please re-write the question: Use brackets to make clear what is an exponent, a factor, a summand, ...
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  3. #3
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    thank you so much, that is abolutely fantastic!

    No 3:



    <br /> <br />
f(x)= xe^2x + 10x <br />

    Its still not printing out properly (new to the math function) but it should bw xe to the power of 2x - hope you can make sense of this - thank you so much.
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  4. #4
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    Quote Originally Posted by tangehayes View Post
    thank you so much, that is abolutely fantastic!

    No 3:



    <br /> <br />
f(x)= xe^{2x} + 10x <br />

    Its still not printing out properly (new to the math function) but it should bw xe to the power of 2x - hope you can make sense of this - thank you so much.
    1. Click on the equation in the quote to see how to type composed exponents.

    2. Use product rule with chain rule:

    f(x)= xe^{2x} + 10x~\implies~f'(x)=e^{2x} \cdot 1 + x \cdot e^{2x} \cdot 2 + 10 = e^{2x}(2x+1)+10
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