Sun K.

asked • 05/18/13

Please evaluate this?

Evaluate (d^100/(dx^95 dy^2 dx^3))(ye^x(x)+cos(x)).

Sun K.

I don't get it. Where did the first part go?

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05/19/13

George C.

For the first 3 differentiations, y is a constant.  For the second two differentiations, x is held constant, so the function vanishes.  If you agree that the  sin term vanishes after the first differentiation wrt y, then you must agree the first term vanishes after the second differentiation wrt y.

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05/19/13

Sun K.

What's y1?

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05/22/13

George C.

Rather than take precious time fiddling with subscripts, I noted that the first derivative wrt x was f(x1).  Respectively, the first derivative wrt to y is f(y1).  It is just a shorthand to eliminate having to use the subscripts from the dropdown menu. 

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05/22/13

1 Expert Answer

By:

George C. answered • 05/18/13

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Humboldt State and Georgetown graduate

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f = ye^x(x)+cos(x).             Subscripts are  tedious.  Let f(xn) be the nth derivative wrt  x.

f(x1) = y(xe^x + e^x) - sin x

f(x2) = y(xe^x + 2e^x) - cos x

f(x3) = y(xe^x + 3e^x) + sin x

f(x3)(y1) = (xe^x + 3e^x)

f(x3)(y2) = 0

All derivatives after this are zero.

 

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