Not sure if you mean to ask for the first order partial derivatives, one wrt x and the other wrt y, or the second order partial derivative, first wrt x then wrt y. I'll assume the former.
\(\dfrac\partial{\partial x}(2x+3y)^{10}=10(2x+3y)^9\times2=20(2x+3y)^9\)
\(\dfrac\partial{\partial y}(2x+3y)^{10}=10(2x+3y)^9\times3=30(2x+3y)^9\)
Or, if you actually did want the second order derivative,
\(\dfrac{\partial^2}{\partial y\partial x}(2x+3y)^{10}=\dfrac\partial{\partial y}\left[20(2x+3y)^9\right]=180(2x+3y)^8\times3=540(2x+3y)^8\)
and in case you meant the other way around, no need to compute that, as \(z_{xy}=z_{yx}\) by Schwarz' theorem (the partial derivatives are guaranteed to be continuous because \(z\) is a polynomial).
