Practice question · Select all that apply
y is a function of x. Select every derivative with respect to x that is CORRECT.
Hints
- Scan for any y-term that has been differentiated without a dy/dx attached.
- 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.
Practise Related Rates and Implicit Differentiation
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