Question

Please help

Rewrite in index notation and then differentiate. Answer in the same form as the question.

`y=-5x^2 √(x)`

I think that
`y=-5x^2(x)^(1)/(2)`
is the first part rewriteing in index notation if u could tell me if I am right then differentiate just show each step as I know how to differentiate I just for some reason can get this question right.

Answer 1

I hope I've finally done justice to it.

Explanation:

`y=-5x^2 √(x)`

`y=-5x^2(x)^(1)/(2)`

`y=-5( {x}^{2 + (1)/(2) }) = - 5 {x}^{ (5)/(2) }`

`(dy)/(dx) = - 5( (5)/(2)) {x}^{ (5)/(2) - 1 }`

`(dy)/(dx) = ( ( - 25)/(2)) {x}^{ (3)/(2) }`

`(dy)/(dx) = ( ( - 25)/(2)) \sqrt[3]{ {x}^(2) }`