Function g(x,y) has the form: g(x,y)=cos(xπy)+log3(x−y)1=cos(xπy)+ln(x−y)ln(3).
We receive:
∂y∂g=−2yxπsin(xπy)+(ln(x−y))2ln(3)⋅x−y1. ∂y∂x∂2g=−2yπsin(xπy)−2xπ2cos(xπy)−(ln(x−y))3(ln(3))(2+ln(x−y))⋅(x−y)21.
Answer: ∂y∂x∂2g=−2yπsin(xπy)−2xπ2cos(xπy)−(ln(x−y))3(ln(3))(2+ln(x−y))⋅(x−y)21
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