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

Trigonometric Functions - differentiation - basic expressions.
Test Yourself 2 - Solutions.


 

Simple differentiation 1.

2. 5 cos (2 - x2)

= -5 sin (2 - x2)(-2x)

= 10xsin (2 - x2)
  3. 4. -12x2cos (3 - 4x3)
  5. y' = -15 sin 5x - 15 cos 5x 6. y' = 2π sec2πx - 3e sin ex
Chain rule 7. y = tan2 x

y' = 2tanx sec2 x

 8. y = 3(1 + 2sin x)3

y' = 3×3(1 + 2 sin x)2 × 2cos x

=18cos x(1 + 2 sin x)2
  9. y = cos(sin 3x)

y' = -sin (sin 3x)× (cos3x) × 3

= -3 cos 3x (sin (sin 3x))

 10.
  11. 12.
Product rule. 13. 14.
  15. 16.
  17. y = πx sin πx

y' = π sin πx + π2x cos πx

 18.
Quotient rule. 19. 20.
  21.

22.

 

23.

  24.