Differentiation techniques
Lesson 7 of 11
Product and quotient rules
Objective. Differentiate products and quotients of functions.
The key idea
For uv the derivative is u′v + uv′. For u/v it is (u′v − uv′)/v². The order matters in the quotient rule.
Worked example
Differentiate y = x²e^x.
- 1u = x², u′ = 2x.
- 2v = e^x, v′ = e^x.
- 3u′v + uv′ = 2xe^x + x²e^x = xe^x(2 + x).
Answer: xe^x(x + 2)
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Reversing the subtraction in the quotient rule numerator.
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