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y-xsin-x-d-35-y-dx-35-

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Question Number 178847 by zaheen last updated on 22/Oct/22
y=xsin (x) (d^(35) y/dx^(35) )=?
y=xsin(x)d35ydx35=?
Answered by mr W last updated on 22/Oct/22
y=f(x)g(x) with f(x)=x, g(x)=sin (x) f^((0) (x)=x,f^((1)) (x)=1, f^((k)) (x)=0 for k≥2 g^((0) (x)=sin x, g^((1)) (x)=cos x, g^((2)) (x)=−sin x g^((2k+1)) (x)=(−1)^k cos x, g^((2k)) (x)=(−1)^k sin x y^((35)) =f^((0)) (x)g^((35)) (x)+35f^((1)) (x)g^((34)) (x)+0 =x(−cos x)+35(1)(−sin x) =−x cos x−35 sin x
y=f(x)g(x)withf(x)=x,g(x)=sin(x)f(0(x)=x,f(1)(x)=1,f(k)(x)=0fork⩾2g(0(x)=sinx,g(1)(x)=cosx,g(2)(x)=−sinxg(2k+1)(x)=(−1)kcosx,g(2k)(x)=(−1)ksinxy(35)=f(0)(x)g(35)(x)+35f(1)(x)g(34)(x)+0=x(−cosx)+35(1)(−sinx)=−xcosx−35sinx
Commented by Tawa11 last updated on 23/Oct/22
Great sir
Greatsir

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