Mathematics I / Related Rates and Implicit Differentiation
Practice question · Select all that apply

y is a function of x. Select every derivative with respect to x that is CORRECT.

Hints
  1. Scan for any y-term that has been differentiated without a dy/dx attached.
  2. the first option needs the product rule AND the chain rule on the y-factor.
Show the answer
  • B. Differentiating y squared with respect to x brings a dy/dx factor with it.
  • D. In related rates, every changing quantity carries a d/dt factor.
  • E. The derivative of x squared times y is 2xy plus x squared times dy/dx.
Why

Options 3 and 5 both drop a dy/dx: the correct results are cos y times dy/dx, and y squared plus 2xy dy/dx. Option 2 shows the product rule applied correctly, with the chain rule supplying the dy/dx only on the y-factor.

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