Differentiating Products And Quotients
Muhtasari
You can differentiate simple powers, but real functions are often built by multiplying or dividing two expressions together. To differentiate these you need two new tools: the product rule and the quotient rule. They are the natural next step once basic differentiation is secure.
In this lesson you will learn the product rule \((uv)'=u'v+uv'\) and the quotient rule \(\left(\frac{u}{v}\right)'=\frac{u'v-uv'}{v^2}\), and apply them to worked examples. The key skill is identifying the two pieces, differentiating each, and assembling the result in the correct order, especially the subtraction in the quotient rule.
Malengo
- Differentiate products and quotients of functions.
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- The product rule for y = uv states that dy/dx equals: A. u'v' B. u'v + uv' C. u'v - uv' D. (u'v - uv')/v^2 Answer: B
- The quotient rule for y = u/v states that dy/dx equals: A. (u'v + uv')/v^2 B. (u'v - uv')/v^2 C. (uv' - u'v)/v^2 D. u'/v' Answer: B
- Differentiate y = x^2(2x + 1). A. 4x + 1 B. 6x^2 + 2x C. 2x^2 + 2x D. 6x^2 + 1 Answer: B
- Differentiate y = x/(x + 1). A. 1 B. 1/(x + 1) C. 1/(x + 1)^2 D. x/(x + 1)^2 Answer: C
- In the quotient rule, the denominator of the result is: A. v B. v^2 C. u^2 D. uv Answer: B
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