Question

Find \(\frac{\partial z}{\partial x}\)  where \(z=ax^2+2by^2+2bxy\).

(a) 3by

(b) 2ax

(c) 3(ax+by)

(d) 2(ax+by)

I have been asked this question by my college professor while I was bunking the class.

This is a very interesting question from First Order PDE topic in chapter Partial Differential Equations of Engineering Mathematics

Answer 1

The correct choice is (d) 2(ax+by)

The best explanation: Here we use partial differentiation.

\(z=ax^2+2by^2+2bxy\).

\(\frac{\partial z}{\partial x}\)=a(2x)+0+2by

\(\frac{\partial z}{\partial x}\)=2ax+2by

\(\frac{\partial z}{\partial x}\)=2(ax+by).