Question

Find the derivative of the following function, with a positive index (differentiation)

pls help there’s a picture

Answer 1

2nd option

Explanation:

Using the power rule

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

Given

f(x) =
`\frac{3}{2\sqrt[3]{x} }` =
`\frac{3}{2x^{(1)/(3) } }` =
`(3)/(2)`
`x^{-(1)/(3) }` , then

f'(x) = -
`(1)/(3)` ×
`(3)/(2)`
`x^{-(4)/(3) }`

= -
`(1)/(2)` ×
`\frac{1}{x^{(4)/(3) } }`

= -
`\frac{1}{2x^{(4)/(3) } }` = -
`\frac{1}{2\sqrt[3]{x^4} }` [ Note there should be a leading negative ]