Question

Differentiate sin^4 x with respect to x^3?

Answer 1

`(du)/(dv)=(4sin^3xcosx)/(3x^2)`

Explanation:

Let,

`u=sin^4 x, and v=x^3`

Differentiate `sin^4 x` with respect to `x^3`

i.e. Differentiate `u` with respect to `v=>(du)/(dv)`

So, `(du)/(dx)=4sin^3xcosx and (dv)/(dx)=3x^2`

Thus,

`(du)/(dv)=((du)/(dx))/((dv)/(dx))=(4sin^3xcosx)/(3x^2)`