Question

How do you differentiate `sqrt(2x^3 - 3x- 4)`?

Answer 1

`(3(2x^2-1))/(2sqrt(2x^3-3x-4))`

Explanation:

This can be rewritten as `(2x^3-3x-4)^(1/2)`.

According to the chain rule, `d/dx(u^(1/2))=1/2u^(-1/2)*(du)/dx`.

Thus,

`d/dx(2x^3-3x-4)^(1/2)=1/2(2x^3-3x-4)^(-1/2)d/dx(2x^3-3x-4)`

`=>1/(2sqrt(2x^3-3x-4))*(6x^2-3)`

`=>(3(2x^2-1))/(2sqrt(2x^3-3x-4))`