How exactly do you determine dy / dx ?

Question

Maybe for this one: y = 2 / 3(x)^3

Answer 1

You memorize the standard forms: In this case

if y=a x^b where b is any +- number

dy/dx= b*a* x^b-1

here is an example:

y= 1/sqrt(x^2+1)

y= (x^2+1)^-.5

let u= x^2+1

dy/du= -.5 (u)^-1/5

dy/dx= dy/du*du/dx= -.5(x^2+1)^-1.5 * 2x

because du/dx= d (x^2+1)/dx= 2x