Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Trigonometric Functions - differentiation - basic expressions.
Test Yourself 1 - Solutions.



Differentiate each of the following with respect to x unless indicated otherwise. Express your answers in the nicest possible way :)

Simple differentiation 1. y = 5 + 2sin 3x - 4cos 5x

y' = 2×3cos 3x - 4×5(-sin 5x)

= 6cos3x + 20sin5x

 2. y = 3sin 8x

y' = 3× 8 cos 8x

= 24 cos 8x
  3. y = sec x

4. Differentiate y = sin π with respect to x.

As there is no x term, sin π is a constant.

So the derivative is 0.
  5.

6.
  7. 8.
Chain rule 9. y = (tan 3x)2

y' = 2(tan 3x)1 × sec2 3x × 3

= 6 tan 3x sec2 3x

 10. y = sec2 x

  11. y = (cos x + sin 2x)3

y' = 2(cos x + sin 2x)2 ×

(-sin x + cos 2x × 2)

= 2(cos x + sin2x)2(2cos2x - sinx)

 12. y = (2 - cos 2x)2

y' = 2(2 - cos 2x) × 2sin2x

= 4 sin2x (2 - cos 2x)
  13.

14.
Product rule. 15. 16.
  17. 18.
  19. 20. " express in the simplest factored form".
Quotient rule. 21. 22.
  23.

24. Differentiate

  25. Differentiate .

26. Differentiate .