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Calculus Help!?

Find the derivative of f when

f(x) = tan(x) (3 + 8 csc(x))

---- this part is easy, I am having difficulty with the getting the right multiple choice answer. Is there a good way to figure this out -----

Find the derivative of f when

f(x) = tan(x) (3 + 8 csc(x))

---- this part is easy, I am having difficulty with the getting the right multiple choice answer. Is there a good way to figure this out -----

1. f′(x) = csc^2(x) (3 + 8 sin(x))

2. f′(x) = sec^2(x) (3 + 8 sin(x))

3. f′(x) = csc^2(x) (3 − 8 cos(x))

4. f′(x) = sec^2(x) (3 sin(x) + 8)

5. f′(x) = csc^2(x) (3 sin(x) + 8)

6. f′(x) = sec^2(x) (3 − 8 sin(x))

Thanks in advance

1 Answer

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    tan(x) * (3 + 8 * csc(x))

    3 * tan(x) + 8 * sec(x)

    Derive

    3 * sec(x)^2 + 8 * sec(x) * tan(x) =>

    sec(x) * (3 * sec(x) + 8 * tan(x)) =>

    sec(x) * (3/cos(x) + 8 * sin(x)/cos(x)) =>

    sec(x)^2 * (3 + 8 * sin(x))

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