Partial Derivatives MCQ | Calculus for AI Multiple Choice Questions

Direction: Choose the correct option

What is a partial derivative?

A. Derivative of a composite function

B. None

C. Derivative with respect to one variable, treating others constant

D. Derivative of a partial function

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For f(x,y)=x^2 + y^2, what is ∂f/∂x?

A. 2y

B. 2x

C. y

D. x

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The notation ∂f/∂y represents:

A. Second derivative

B. Partial derivative with respect to y

C. Total derivative

D. Gradient component in x

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For f(x,y)=3xy, ∂f/∂x = ?

A. 3y

B. 3

C. 0

D. 3x

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Higher-order partial derivatives are useful for:

A. Hessian matrix

B. Taylor series

C. Gradient descent

D. Jacobian

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