Question

Find the gradient of V = x^2 sin(y)cos(z).

(a) 2x siny cos z ax + x^2 cos(y)cos(z) ay – x^2 sin(y)sin(z) az

(b) 2x siny cos z ax + x^2 cos(y)cos(z) ay + x^2 sin(y)sin(z) az

(c) 2x sinz cos y ax + x^2 cos(y)cos(z) ay – x^2 sin(y)sin(z) az

(d) x siny cos z ax + x^2 cos(y)cos(z) ay – x^2 sin(y)sin(z) az

The question was asked in an online quiz.

My doubt is from Gradient of a Function and Conservative Field in section Vector Differential Calculus of Engineering Mathematics

Answer 1

Correct answer is (a) 2x siny cos z ax + x^2 cos(y)cos(z) ay – x^2 sin(y)sin(z) az

Explanation: \(V = x^2 sin(y)cos(z) \)

Gradient of \(V = \frac{∂V}{∂x} a_x + \frac{∂V}{∂y} a_y + \frac{∂V}{∂z} a_z \)

\(= 2x siny cos z a_x + x^2 cos(y)cos(z) a_y – x^2 sin(y)sin(z) a_z \)