Question

Find first derivative f(x)= x² - 4 /x³ + 9 ​

Answer 1

f'(x) = 2x +
`(12)/(x^(4) )`

Explanation:

differentiate using the power rule

`(d)/(dx)` ( a
`x^(n)` ) = na
`x^(n-1)`

Given

f(x) = x² -
`(4)/(x^3)` + 9 = x² - 4
`x^(-3)` + 9 , then

f'(x) = 2x + 12
`x^(-4)` = 2x +
`(12)/(x^(4) )`

Answer 2

`f'(x)=2x+(12)/(x^4)`

Explanation:

`f(x)=x^2-(4)/(x^3)+9`

Apply exponent rule
`(1)/(a^b)=a^(-b)`:

`\implies f(x)=x^2-4x^(-3)+9`

Differentiate using the power rule
`(d)/(dx)(x^a)=a \cdot x^(a-1)` :

`\implies f'(x)=2 \cdot x^(2-1)-(-3)4x^(-3-1)+0`

`\implies f'(x)=2x+12x^(-4)`

`\implies f'(x)=2x+(12)/(x^4)`