Find the derivative of the Function: P(x) = (x - 3cosx)(x + 3cosx)

Chaya Galloway 2021-01-15 Answered
Find the derivative of the Function: P(x)=(x3cosx)(x+3cosx)
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Expert Answer

dessinemoie
Answered 2021-01-16 Author has 90 answers
P(x)=(x3cosx)(x+3cosx)=x29cos2(x)
dpdx=2x9d(cos2x)=2x92cosxd(cosx)=
=2x92cosx(sinx)
=2x+92sinxcosx
=2x+9sin(2x)
you can use the formula
(ab)(a+b)=a2b2
2sinxcosx=sin(2x)
or you can use the product rule
dpdx=(d(x3cosx))(x+3cosx)+(x3cosx)(d(x+3cosx))=
(1+3sinx)(x+3cosx)+(x3cosx)(13sinx)=
x+3cosx+3xsinx+9sinxcosx+x3cosx3xsinx+9sinxcosx=
2x+18sinxcosx=2x+92sinxcosx=2x+9sin(2x)
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