Verified answer

[d/dx(6 cotx)]/(cosec2x)

Breaking the problem into 2 halves

1st half

d/dx(6cotx) = 6 d/dx(cotx)

= 6(- cosec^2x) = -6cosec^2x

2nd half

cosec2x = 1/sin2x

since sin2x = 2 sinx cosx

cosec2x = 1/2sinxcosx

cosec2x = (cosecx secx)/2

Now

[d/dx(6 cotx)]/(cosec2x)

=(- 6 cosec^2x)/[(secx cosecx )/2]

=(-12 cosecx)/(secx)

= - 12 cotx

So i think the denominator is also cosec^2x and not cosec2x

Then the equation would be

- 6 cosec^2x/cosec^2x

= -6---- (Constant)

Is the denominator csc 2x or csc^2 x? I'll assume the latter.

The derivative of 6 cot x is 6 * - csc^2 x = -6 csc^2 x.

The denominator is also csc^2 x. Cancel the csc^2 x in the denominator with the csc^2 x in the numerator. That leaves you with -6.

Therefore, the constant number is -6.

I hope that helps. :)

ILoveMaths07.

First step: [d/dx]cot x = - csc^2 x.