Question

Find \(\frac{\partial z}{\partial x}\)  where \(z=sin⁡x^2×cos⁡y^2\).

(a) 2xsin⁡x^2

(b) x sin2x

(c) 2xsin⁡x^2 cos⁡y^2

(d) 6xsin⁡x^2 cos⁡y^2

I have been asked this question during an internship interview.

I'm obligated to ask this question of First Order PDE topic in portion Partial Differential Equations of Engineering Mathematics

Answer 1

The correct choice is (c) 2xsin⁡x^2 cos⁡y^2

Best explanation: Here we use partial differentiation.

z=sin⁡x^2×cos⁡y^2

\(\frac{\partial z}{\partial x}=(cos⁡x^2×2x)× cos⁡y^2\)

\(\frac{\partial z}{\partial x}=2xsin⁡x^2 cos⁡y^2\).