Mathematics · University
Differentiate a polynomial-exponential product
Differentiate before substituting. The value at zero can hide a nonzero product-rule term.
Method and conditions
Differentiate before substituting. The value at zero can hide a nonzero product-rule term.
(uv)' = u'v + uv'
Worked examples
For f(x) = (2x + 1)e^(5x), calculate f′(0). Round the final result to 4 decimal places if needed.
f′(x) = [2 + 5(2x + 1)]e^(5x). At x = 0, this is 2 + 5.
7
For f(x) = (8x + 9)e^(4x), calculate f′(0). Round the final result to 4 decimal places if needed.
f′(x) = [8 + 4(8x + 9)]e^(4x). At x = 0, this is 8 + 36.
44
Try it
For f(x) = (9x + 10)e^(8x), calculate f′(0). Round the final result to 4 decimal places if needed.
For f(x) = (3x + 12)e^(4x), calculate f′(0). Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 89
f′(x) = [9 + 8(9x + 10)]e^(8x). At x = 0, this is 9 + 80.
- 51
f′(x) = [3 + 4(3x + 12)]e^(4x). At x = 0, this is 3 + 48.
Further reading and review references
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