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## Homework Statement

Using the chain rule, prove that d/dx(cotx)= -csc^2x

## Homework Equations

Chain rule

## The Attempt at a Solution

Is this correct?

f(x)=cotx=(tanx)^(-1)

Let f(x) = (x)^-1 Therefore, f'(x)= -1/(x^2)

Let g(x) = tanx Therefore, g'(x)= sec^2x

F'(x)=f'(g(x))g'(x)

=(-1/(tanx)^2)(secx^2)

=(-secx^2)/(tanx^2)

= -csc^2 x