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## Main Question or Discussion Point

I keep getting the wrong answer when i try to differentiate cotx..

this is what i get:

cotx = 1/tanx =cosx/sinx=cosx ⋅ sin^-1

so by the product and chain rule we have:

sinx⋅(sin x)^-1+cos⋅(-1sin^2 x)^-1 ⋅(cosx)^-1

=

sinx/sinx - cosx/cosx ⋅ sin^2x

=1-1/sin^2 x

where as the correct answer is -1/sin^2x = -csc^2 x

could someone please tell me where i am going wrong?

many thanks

Ryan

this is what i get:

cotx = 1/tanx =cosx/sinx=cosx ⋅ sin^-1

so by the product and chain rule we have:

sinx⋅(sin x)^-1+cos⋅(-1sin^2 x)^-1 ⋅(cosx)^-1

=

sinx/sinx - cosx/cosx ⋅ sin^2x

=1-1/sin^2 x

where as the correct answer is -1/sin^2x = -csc^2 x

could someone please tell me where i am going wrong?

many thanks

Ryan