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2) y’ = -5csc x cot x

3) y’ = -5csc x cot x tan x + 5csc x sec² x = 5csc x (sec² x – 1)

4) y’ = (-5csc x cot x tan x – 5 csc x sec² x)/(tan² x) = -5 csc x (tan² x)/(tan² x) = -5 csc x

5) y’ = - sin x/cos x = - tan x

6) y’ = cos x ln (sin x) + sin x cos x/sin x = cos x [ln (sin x) + 1]

7) y’ = (cos x tan x + sin x sec² x)(e^{sin x tan
x})

8) y’ = 2xsec x² sec² (sec x²)

9) y’ = 3tan² x sec² x

10) y’ = (15x²)5sin⁴ 5x³ = 75x²sin⁴ 5x³

11) y’ = 7(5ln x + 5)cos (5xln x)

12) y’ = 14x sin (5xln x) + 7x²(5ln x + 5)cos (5xln x)

13) y’ = 35(ln e^2x)(2e^2x/e^2x) [tan² (xcos 4x)] + 7(ln e^2x)5[2tan (xcos 4x)][sec² (xcos 4x)](cos 4x - 4xsin 4x)
I hope you don’t see such a problem on a test!

14) y’ = [(sin x²)/x – 2xsin x² ln x]/sin² x²

15) y’ = -2sin^-3 x

16) y’ = e^x(3/2)sin^1/2e^x

Answers – Trig in Calculus