Question

Given √x + y = 2x³, find dy/dx

Answer 1

`(dy)/(dx) = 6x^2 - (1)/(2√(x) ) }`

Explanation:

-
`√(x)` is the same as
`x^{(1)/(2) }`, so that can be replaced to make its derivative easier to calculate.

`x^(1)/(2) + y = 2x^3`

- the power rule can be used for
`x^(1)/(2)` and
`2x^3`

- the derivative of y is just
`(dy)/(dx)`

`(1)/(2) x^(-1)/(2) + (dy)/(dx) = 6x^2`

- now solve for
`(dy)/(dx)` and simplify

`(dy)/(dx) = 6x^2 - (1)/(2) x^(-1)/(2)`

`(dy)/(dx) = 6x^2 - ((1)/(2) )/(x^(1)/(2) )`

`(dy)/(dx) = 6x^2 - (1)/(2√(x) ) }`