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The gradient of the function ( f(x, y) = sin x + cos y ) is given by the vector of its partial derivatives.
First, we calculate the partial derivative with respect to ( x ):
[
frac{partial f}{partial x} = cos x
]
Next, we calculate the partial derivative with respect to ( y ):
[
frac{partial f}{partial y} = -sin y
]
Therefore, the gradient ( nabla f ) is:
[
nabla f = left( frac{partial f}{partial x}, frac{partial f}{partial y} right) = left( cos x, -sin y right)
]
So, the gradient of the function ( sin x + cos y ) is:
[
nabla f = (cos x, -sin y)
]
Answer: a
Explanation: Grad (sin x + cos y) gives partial differentiation of sin x+ cos y with respect to x and partial differentiation of sin x + cos y with respect to y and similarly with respect to z. This gives cos x i – sin y j + 0 k = cos x i – sin y j.