Differentiation rules practice question 26
A student finds for the function below as shown. Find the first line that is wrong.
Both brackets change when x changes. How many terms does the derivative of a product have?
Expand f first and differentiate the polynomial, then compare with line 1.
Theory UBC Math 100 §4.1CLP-1 §2.4Key results
Corrected working
Strategy
Product rule: differentiate each factor in turn and add. Expanding first gives the same answer.
Working
u′v + uv′.
Substitute x = 1.
Answer
The answer is f prime of 1 equals 0.
Check
f(0.99) and f(1.01) are both about −1.9993, just above f(1) = −2, so f bottoms out at x = 1 and f′(1) = 0 fits.
Where this goes wrong
Differentiating one factor and leaving the other alone. The product rule has two terms because both factors change with x.
The idea behind it
The differentiation rules lesson, a figure to move, in a few steps
Try a similar question
Let . Find .Saved in this browser only.