How do you find the derivative of \cot x ?

tebollahb 2021-12-18 Answered
How do you find the derivative of cotx ?
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Thomas White
Answered 2021-12-19 Author has 40 answers
Explanation:
y=cotx
y=1tanx
y=1sinxcosx
y=cosxsinx
Letting y=g(x)h(x), we have that g(x)=cosx and h(x)=sinx
y=g(x)×h(x)g(x)×h(x)(h(x))2
y=sinx×sinx(cosx×cosx)(sinx)2
y=sin2x+cos2xsin2x
y=(sin2x+cos2x)sin2x
y=1sin2x
y=csc2x
Hopefully this helps!

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kalfswors0m
Answered 2021-12-20 Author has 24 answers

As per trigonometric identities, cot x can also be written as cosxsinx
Now we can use quotient rule of differentiation to find the derivative of cotx.
dcotxdx=d(cosxsinx)dx
Quotient rule: d(uv)dx=(vdudxudvdx)v2
Here u=cosx, v=sinx
We can substitute the formulae for the derivatives of sin x and cos x given by
d(cosx)dx=sinx and d(sinx)dx=cosx
On putting the above values in equation (ii), we get
d(cotx)dx=sinxsinxcosxcosxsin2x
=(sin2x+cos2x)sin2x
=1sin2x
=(csc2x)
d(cotx)dx=csc2x

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