Question

The value of \(\frac{∂z}{∂y}\)=8x^2+6xy^2+4. What is the function z expressed as?

(a) z=8x^3+2x^2 y^2+4x

(b) z=8x^2 y+2xy^3+4y

(c) z=8y+2xy^2+4y

(d) z=16x+6y^2

This question was addressed to me in an interview for job.

Enquiry is from Variable Treated as Constant topic in division Partial Differentiation of Engineering Mathematics

Answer 1

The correct choice is (b) z=8x^2 y+2xy^3+4y

The best I can explain: Since the given partial differentiation is with respect to y, to find the expression for the function z, we need to integrate the given partial differentiation expression with respect to y.

Therefore, \(∫\frac{∂z}{∂y}.dy\)=∫(8x^2+6xy^2+4).dy

               z=8x^2 y+\(\frac{6}{3}\) xy^3+4y

               z=8x^2 y+2xy^3+4y