Question #b8918

1 Answer
Jul 16, 2017

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)