Derivative of a product of trig functions: 3sin⁡(x)cot⁡(x) −3cos⁡xsin2x

Arely Briggs

Arely Briggs

Answered

2022-01-24

Derivative of a product of trig functions: 3sin(x)cot(x)
3cosxsin2x

Answer & Explanation

Maritza Mccall

Maritza Mccall

Expert

2022-01-25Added 17 answers

You need to use the product rule:
(3sinxcotx)=
3(sinx)cotx+3sinx(cotx)=
3cosxcotx+3sinx(csc2x)=
3cosxcotx3sinxcsc2x=
3cosxcosxsinx3sinx1sin2x=
3cos2xsinx31sinx=
31sinx(cos2x1)=
31sinx(1sin2x1)=3sinx
A much simpler way to do this, as was mentioned in the comments section, is to notice that 3sinxcotx=3sinxcosxsinx=3cosx which is trivial to differentiate:
(3cosx)=3(cosx)=3(sinx)=3sinx

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