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Щах
@Щах
July 2022
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Вычислить производную
y=x(sin(lnx)-cos(lnx))
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ShirokovP
Verified answer
y' = (x * (sin(lnx) - cos(lnx)))' =
= (x)'*
(sin(lnx)-cos(lnx)) + x * (sin(lnx) - cos(lnx)) ' =
= sin(lnx) - cos(lnx) + x * ( cos (lnx)*(lnx)' + sin (lnx)* (lnx)' ) =
= sin(lnx) - cos(lnx) + x * ( cos (lnx)/x + sin (lnx)/x ) =
= sin(lnx)
- cos(lnx) + cos (lnx)
+ sin (lnx) =
= 2 sin(lnx)
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Answers & Comments
Verified answer
y' = (x * (sin(lnx) - cos(lnx)))' == (x)'* (sin(lnx)-cos(lnx)) + x * (sin(lnx) - cos(lnx)) ' =
= sin(lnx) - cos(lnx) + x * ( cos (lnx)*(lnx)' + sin (lnx)* (lnx)' ) =
= sin(lnx) - cos(lnx) + x * ( cos (lnx)/x + sin (lnx)/x ) =
= sin(lnx) - cos(lnx) + cos (lnx) + sin (lnx) =
= 2 sin(lnx)