The Chain Rule MCQ | Calculus for AI Multiple Choice Questions

Direction: Choose the correct option

What does the chain rule compute?

A. Derivative of a sum

B. Derivative of a product

C. Derivative of a composite function

D. Derivative of a quotient

Direction: Choose the correct option

If y = f(u) and u = g(x), then dy/dx = ?

A. du/dx * dx/du

B. dy/du * du/dx

C. None

D. du/dy * dx/du

Direction: Choose the correct option

For h(x)=sin(x^2), what is h'(x)?

A. 2x sin(x^2)

B. cos(2x)

C. 2x cos(x^2)

D. cos(x^2)

Direction: Choose the correct option

The chain rule is essential in backpropagation for

A. Neural networks

B. Decision trees

C. Linear regression

D. Logistic regression

Direction: Choose the correct option

If z = f(x,y) and x = g(t), y = h(t), then dz/dt = ?

A. ∂f/∂x * dx/dt + ∂f/∂y * dy/dt

B. (dx/dt)*(dy/dt)

C. ∂f/∂x + ∂f/∂y

D. None

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