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Thread: derivitives

  1. #1
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    derivitives

    a) $\displaystyle f(x)=1/sin(x)$
    b) $\displaystyle g(x)= ln(x^2)$

    find the derivitives....just need to confirm.

    i have worked through the questions and i for a) i get $\displaystyle (-cos(x))/sin(x)^2$ by using the quotient rule. but when i try differentiate on a computer software i get $\displaystyle -1/sin(x)^2*cos(x)$....are they the same????

    and for the second one i know that the answer is $\displaystyle 2/x$since ln(x) = 1/x. but not sure how to show the working...any help would be appreciated.

    thanks
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  2. #2
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    Quote Originally Posted by b00yeah05 View Post
    a) $\displaystyle f(x)=1/sin(x)$
    b) $\displaystyle g(x)= ln(x^2)$

    find the derivitives....just need to confirm.

    i have worked through the questions and i for a) i get $\displaystyle (-cos(x))/sin(x)^2$ by using the quotient rule. Mr F says: Correct.

    but when i try differentiate on a computer software i get $\displaystyle -1/sin(x)^2*cos(x)$....are they the same???? Mr F says: Yes. $\displaystyle -\frac{1}{\sin^2 x} \times \cos x = -\frac{\cos x}{\sin^2 x}$.

    and for the second one i know that the answer is $\displaystyle 2/x$since ln(x) = 1/x. but not sure how to show the working...any help would be appreciated.

    thanks
    For the second one, you could use the fact that $\displaystyle \ln x^2 = 2 \ln x$. And you know the derivative of $\displaystyle \ln x$ .....

    Recall log rule: $\displaystyle \ln a^n = n \ln a$.
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