(a) f(x) = (x^4+ 3x^2 – 2)^50 (b) f(x) = (1+ x^4 )^2/3

Tentukanlah turunan pertama dari setiap fungsi berikut:

(a) f(x) = (x^4+ 3x^2-2)^50

(b) f(x) = (1+ x^4 )^(2/3)

Jawab

(d [ f(x) ]^n)/dx=(n[f(x) ]^(n-1) ) ( f^’ (x))

Maka :

(a).

(d [x^4+ 3x^2-2)^50])/dx=[50(x^4+ 3x^2-2)^49] ( 4x^3+ 6x) = 50( 4x^3+ 6x) (x^4+ 3x^2-2)^49

(b).

(d [(1+ x^4 )^(2/3)] )/dx=[2/3(1+ x^4 )^(-1/3) ] ( 4x^3) = ( 2/(3(1+ x^4 )^(1/3) ) ) ( 4x^3) = (8x^3)/(3(1+ x^4 )^(1/3) ) = (8x^3)/(3√(3&1+ x^4 ))

for more detailed writing click on the following link Tentukanlah turunan pertama dari setiap fungsi berikut: f(x) = (x^4+ 3x^2-2)^50 f(x) = 〖(1+ x^4 )〗^(2/3)

f(θ) = (e )^(sec 3θ)

Tentukanlah turunan pertama : f(θ) = (e )^(sec 3θ) !

Jawab :

d (e)^f(θ)/dx= e^f(θ) d[f(θ) ]/dx

Maka :

d [(e )^(sec 3θ)]/dx= e^(sec 3θ) d( sec 3θ)/dx = e^(sec 3θ) 3 sec 3θ tan 3θ = 3e^(sec 3θ) sec 3θ tan 3θ

for more detailed writing click on the following link Tentukanlah turunan pertamanya : f(θ) = (e )^(sec 3θ) !

f(x) = (e )^(sin x)

Tentukanlah turunan pertama : f(x) = (e )^(sin x) !

Jawab :

d (e)^f(x)/dx= e^(sin x) (d[f(x) ]/dx)

Maka :

d [(e )^(sin x)]/dx= e^(sin x) (d( sin x))/dx = e^(sin x)  cos x

for more detailed writing click on the following link Tentukanlah turunan pertamanya : f(x) = (e )^(sin x) !

f(x) = (x^3- 1)^1000

Tentukanlah turunan pertaman: f(x) = (x^3- 1)^1000 !

Jawab :

d [ f(x) ]^n/dx=(n[f(x) ]^(n-1) ) ( f^’ (x))

Maka :

d [(x^3- 1)^1000]/dx=(1000[(x^3- 1)]^(1000-1) ) ( 3x^2) = 1000(x^3- 1)^999 ( 3x^2) = 3000x^2 (x^3- 1)^999

for more detailed writing click on the following link Tentukanlah turunan pertamanya : f(x) = (x^3- 1)^1000 !

Turunan pertama dari f(x) = √(x^2+ 1)

Tentukan f(x)^’ dari f(x) = √(x^2+ 1) !

Jawab :

Gunakan aturan rantai

Misalkan: z = x^2+ 1 → dz/dx=2x

Maka : y = √(z ) → dy/dz= 1/(2√(z ))= 1/(2√(x^2+ 1 ))

Maka : f(x)^’= dy/dx=( dy/dz)( dz/dx)=(1/(2√(x^2+ 1 )))(2x) = x/√(x^2+ 1 )

for more detailed writing click on the following link Tentukan f(x)^’ dari f(x) = √(x^2+ 1)