Question

Find the partial derivative of f(x,y,z)=x^2y+6z^3xy

Answer 1

Solution:Partial derivatives:

$\frac{\partial \:}{\partial \:x}\left(x^{2y}+6z^{3xy}\right)=2yx^{2y-1}+18yz^{3yx}\ln \left(z\right)$

$\frac{\partial \:}{\partial \:y}\left(x^{2y}+6z^{3xy}\right)=2x^{2y}\ln \left(x\right)+18xz^{3xy}\ln \left(z\right)$

$\frac{\partial \:}{\partial \:z}\left(x^{2y}+6z^{3xy}\right)=18xyz^{3xy-1}$