Turunan Fungsi Trigonometri

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Turunan Fungsi Trigonometri by Mind Map: Turunan Fungsi Trigonometri

1. Apa Itu?

1.1. Rumus turunan trigonometri berisi persamaan turunan yang melibatkan fungsi-fungsi trigonometri seperti sin, cos, tan, cot, sec dan fungsi trigonometri lainnnya.

2. Aplikasi

2.1. video terlampir

3. Rumus-rumus

3.1. Dasar

3.1.1. y=sin X

3.1.1.1. y' = cos x

3.1.2. y = cos x

3.1.2.1. y' = - sin x

3.1.3. y = sin ax

3.1.3.1. y' = a cos ax

3.1.4. y = cos ax

3.1.4.1. y' = -a sin ax

3.1.5. y = tan x

3.1.5.1. y ' = sec^2 x

3.1.6. y = cotan x

3.1.6.1. y' = -csc^2 x

3.1.7. y = sec x

3.1.7.1. y' = sec x tan x

3.1.8. y = csc x

3.1.8.1. - csc x cotan x

3.2. Perluasan 1

3.2.1. y = sin u

3.2.1.1. y' = cos u . u'

3.2.2. y = cos u

3.2.2.1. y' = - sin u . u'

3.2.3. y = tan u

3.2.3.1. y' = sec^2 u . u'

3.2.4. y = cotan u

3.2.4.1. y' = -csc u . u'

3.2.5. y = sec u

3.2.5.1. y' = sec u tan u . u'

3.2.6. y = csc u

3.2.6.1. y' = - csc u cotan u . u'

3.3. Perluasan 2

3.3.1. y = arc sin x

3.3.1.1. y'= 1/ (1 - x^2)^1/2

3.3.2. y = arc cos x

3.3.2.1. y'= -1/ (1 - x^2)^1/2

3.3.3. y = arc tan x

3.3.3.1. y"= 1/(x^2 + 1)

4. Contoh Soal

4.1. y = sec (2x) maka y' =?

4.1.1. u = 2x maka u' = 2

4.1.1.1. d/du sec u = sec u tan u . u'

4.1.1.1.1. d/dx sec 2x = sec 2x tan 2x . 2

4.2. y = sin (3x + 2) maka y'=?

4.2.1. u = 3x + 2 maka u' = 3

4.2.1.1. d/du sin u = cos u . u'

4.2.1.1.1. d/dx sin (3x + 2) = cos (3x + 2) . 3