Mathematics · University
Differentiate a polynomial-exponential product · formula reference
Differentiate before substituting. The value at zero can hide a nonzero product-rule term.
Formula
Differentiate before substituting. The value at zero can hide a nonzero product-rule term.
(uv)' = u'v + uv'
Worked example
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
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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