Jawabannya f'(x) = 10x√x - 4/x³ - 3

Ingat rumus turunan berikut :

f(x) = ax^n → f'(x) = n·a·x^(n-1)

Konsep eksponen :

1/a^n = a^(-n)

√a = a^(1/2)

a^b · a^c= a^(b+c)

Pembahasannya :

f(x) = 4x²√x + 2/x² - 3x

= 4x²·x^(1/2) + 2·x^(-2) - 3x

= 4·x^(2 + 1/2) + 2·x^(-2) - 3x

= 4·x^(4/2 + 1/2) + 2·x^(-2) - 3x

= 4·x^(5/2) + 2·x^(-2) - 3x

f'(x) = (5/2)·4·x^(5/2 - 1) + (-2) ·2·x^(-2-1) - 3

= 10·x^(5/2 - 2/2) - 4·x^(-3) - 3

= 10x^(3/2) - 4/x³ - 3

= 10x^(2/2 + 1/2) - 4/x³ - 3

= 10x^(1 + 1/2) - 4/x³ - 3

= 10·x·x^(1/2) - 4/x³ - 3

= 10x√x - 4/x³ - 3

Jadi turunan pertama fungsi di atas f'(x) = 10x√x - 4/x³ - 3

Terimakasih sudah bertanya