Question

What is the value of \(\frac{∂^2z}{∂x∂y}\) for the z=3x^2y+5y?

(a) 3xy

(b) 6x

(c) 3x+5

(d) 6xy

I have been asked this question in class test.

Origin of the question is Variable Treated as Constant topic in division Partial Differentiation of Engineering Mathematics

Answer 1

Correct option is (b) 6x

To elaborate: Given: z=3x^2y+5y

\(\frac{∂}{∂x}(\frac{∂z}{∂y})=\frac{∂}{∂x}(3x^2+5)=6x \)