If y = cot(u), dy/dx equals?

If y = cot(u), dy/dx equals?

• A. u' tan(u)
• B. -u' csc^2(u)
• C. u' sec^2(u)
• D. -u' cos(u) sin(u)

Answer: (B)

Applying the chain rule: differentiate cot(u) with respect to its inner variable u, then multiply by du/dx. The derivative of cot(u) with respect to u is -csc^2(u). Multiply by du/dx, which is u'. So the result is -u' csc^2(u). This matches the correct form. If u were simply x, it would be -csc^2(x). The other expressions come from differentiating tan or misapplying the inner derivative, but they do not match the derivative of cot.

Applying the chain rule: differentiate cot(u) with respect to its inner variable u, then multiply by du/dx. The derivative of cot(u) with respect to u is -csc^2(u). Multiply by du/dx, which is u'. So the result is -u' csc^2(u). This matches the correct form. If u were simply x, it would be -csc^2(x). The other expressions come from differentiating tan or misapplying the inner derivative, but they do not match the derivative of cot.