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I have 3 derivatives that I need to find:

1: $ y = 3sin(x) - ln(x) + 2x^\frac{1}{2} $

My answer:

$ 3cos(x) - \frac{1}{x} + (\frac{1}{2}) (2x^\frac{-1}{2}) $

2: $ y = 3e^{2x} * ln(2x + 1) $

My Answer:

$ 3e^{2x} (\frac{2}{2x+1}) + 6e^{2x} (ln(2x+1)) $

3: $y = \frac{sin(2x)}{3x^2 + 5} $

My Answer:

$ \frac{(3x^2 + 5)(2sin(2x)) - sin(2x)(6x)}{(3x^2 + 5)^2} $

I'm relatively positive I did these correctly, but please let me know if I haven't.

EDIT

3: $ \frac{(3x^2 + 5)(2cos(2x)) - sin(2x)(6x)}{(3x^2 + 5)^2} $

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    @DavidMitra The professor has been quite nice about the simplifications. While I could simplify it, he just wants to make sure we know the required steps :)2012-12-12

1 Answers 1

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Note:

In $(3)$: $\cos(2x)$ appears nowhere in your solution. That should tell you something about your solution to $(3)$.
You got it right in $(1)$, so I'm assuming you know that the derivative of $\sin(2x) = 2 \cos(2x)$.

Spend some more time on $(3)$, and see what you arrive at.


I'm assuming you have written intermediate steps, and simply posted your solutions. Be sure that if this is homework, that you hand in a more detailed, step-by-step solution. You can simplify a little bit, too, e.g., in $(1)$.

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    I f$i$gured you had show$n$ your work, a$n$d it is perfectly understandable why you wouldn't want to type it all out!2012-12-12