Question

As derivadas parciais de z= sqrt(x^2+3xy^2) são:

Answer 1

Derivando para x

$\boxed{\frac{\partial\ f}{\partial\ x} = \frac{2x+3y^2}{2\sqrt{x^2+3xy^2}}}$

Derivando para y

$\frac{\partial\ f}{\partial\ y}=\frac{6xy}{2\sqrt{x^2+3xy^2}}\\\\ \boxed{\frac{\partial\ f}{\partial\ y}=\frac{3xy}{\sqrt{x^2+3xy^2}}}$