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Please evaluate this hard derivative?

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

The answer is 0 but I just seem to get super confused with this problem. Please show the work step by step so I won't get lost. I've work on this for a long time.

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1 Answer

∂^2/∂y^2 ((y)(e^x)(x)+cos(x)) = 0

==> (∂^100/(∂x^95 ∂y^2 ∂x^3))((y)(e^x)(x)+cos(x)) = 0, since no matter how many times you take derivative with respect to x, the highest degree in y is 1.