- Difficulty
- Introductory
- Suggested time
- 3 min
- Marks
- 2
Exponential and trigonometric functions practice question 3
Which of the following is the derivative of ?
is one function of times another. Which rule does that call for, and how many terms should its answer have?
This is a product, so the product rule applies: with and .
Theory UBC Math 100 §3.5CLP-1 §2.7Key results
Worked solution
Strategy
A polynomial times an exponential is a product. Use the product rule, then factor out the common eˣ.
Working
u′v + uv′ with u = x², v = eˣ.
Factor out eˣ.
Answer
The answer is x squared plus 2x, all times e to the x.
Check
At x = 1, (h(1.01) − h(0.99))/0.02 ≈ 8.155, which is 3e, as (x² + 2x)eˣ gives, not the 2e ≈ 5.44 of 2xeˣ.
Where this goes wrong
Multiplying the two derivatives, 2x · eˣ. The derivative of a product is not the product of the derivatives; both cross terms are needed.
Leans on
The product rule, from Differentiation rules
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