Question

Question #b8918

Answer 1

`d/(dx) [cot(3x^2-7)] = color(blue)(-6xcsc^2(7-3x^2)`

Explanation:

We're asked to find the derivative

`(dy)/(dx)[y = cot(3x^2-7)]`

`y'(x) = d/(dx)[-cot(7-3x^2)]`

Factor out the `-1`:

`= -d/(dx)[cot(7-3x^2)]`

Use the chain rule:

`d/(dx) [cot(7-3x^2)] = d/(du) [cotu] (du)/(dx)`

where

• `u = 7-3x^2`

• `d/(du)[cotu] = -csc^2u`:

`= -(-csc^2(7-3x^2) d/(dx)[7-3x^2])`

`= csc^2(7-3x^2) d/(dx)[7-3x^2]`

Use power rule:

`= color(blue)(csc^2(7-3x^2)(-6x)`