13) f'(x) = (3 cot x - 2 csc x) [By Linear Property] B) csc x (2 csc x - 3 cot x) D) (3 cot x - 2 csc x) 14) Using Product Rule (fg)' = f'g + fg' find (x cos x) A) sin x + x cos x B) sin x - x cos x C) cos x - x sin x D) cos x + x sin x 15) Find (x cos x - sin x) A) x cos x - sin x B) -x sin x C) x cos x D) sin x - cos x 16) Find (x^2 tan x) A) 2x tan x + x^2 sec^2 x B) (2x sec^2 x - x^2 tan x) / sec^2 x C) 2x sec^2 x + x^2 tan x D) (2x sec^2 x - x^2 tan x) / tan^2 x 17) Find (100 + 4x) A) 100 B) 1 C) 0 D) 4 18) Using Quotient Rule to find g''(100 + 4x) A) 4(100 + 4x)^-2 B) (100 + 4x)^-2 C) 100(100 + 4x)^2 D) 400(100 + 4x)^-2
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Recall that the derivative of $\cot x$ is $-\csc^2 x$ and the derivative of $\csc x$ is $-\csc x \cot x$. So, we have: $f'(x) = 3(-\csc^2 x) - 2(-\csc x \cot x) = \boxed{-3\csc^2 x + 2\csc x \cot x}$ Show more…
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