It's not a good idea to use "x" as the variable here. Use, say, u instead:dylanhouse said: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)
Yes, that is a valid proof.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
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