Question

Q. Find the gradient of the function sin x
+ COS y.
O A. cos xi - sin yj
O B.cos x i + sin yj
O C. sin xi- cos y )
O D. sin xi + cosyj​

Answer 1

Explanation:

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Answer 2

Answer: The gradient of the function sin x + cos y is given by option A) cos xi - sin y j .

Explanation:

Gradient is defined as the rate of change of any quantity i.e. change in position or distance, temperature, etc. depending on the function.

In three dimension gradient is given by

$\frac{d}{dx}i+ \frac{d}{dy} j +\frac{d}{dz} k$

Given function is F = sin x + cos y

Gradient of F = $\frac{d(sinx)}{dx}i + \frac{d (cos y)}{dy} j$

The derivative of sin x and cos y is

$\frac{d(sin x)}{dx} = cos x$

$\frac{d(cos y)}{dy}= -sin y$

Gradient of F = cos xi + (-sin y) j

Gradient of F = cos xi - sin y j

So, the correct option is A) cos xi - sin y j