Find the partial derivative of the dependent variable with respect to each of the independe \[ u=e^{8 x+5 y} \] \( \frac{\partial z}{\partial x}=\square \)

Q. 33. For the function \( u=\log \frac{x^{2}+y^{2}}{x y} \), prove that: \[ \frac{\partial^{2} u}{\partial x \partial y}=\frac{\partial^{2} u}{\partial y \partial x} . \]

\( f(x)=(2x^{5}-x^{3}+3x^{2}-4) \)

3. (15б) Найдите полный дифференциал и полное приращение функции \( z=\sqrt{x y^{2}-y^{3}} \) точке \( A(2,1) \) при \( \Delta x=0,1 \) и \( \Delta y=0,2 \).

Change the order of integration in \( \int_{0}^{a} \int_{x}^{a}\left(x^{2}+y^{2}\right) d y d x \) and hence evaluate it. (OR)

a) Change the order of integration in \( \int_{0}^{0} \int_{0}^{3}\left(x^{2}+y^{2}\right) d y d x \) and hence evaluate it.