Mathematics · University
A Taylor coefficient of an exponential · formula reference
The requested coefficient is not the nth derivative; divide by n factorial.
Formula
The requested coefficient is not the nth derivative; divide by n factorial.
[xⁿ] e^(kx) = kⁿ/n!
Worked example
Find the coefficient of x^3 in the Maclaurin series of 4e^(2x). Round the final result to 4 decimal places if needed.
Use e^(2x) = Σ (2x)^j/j!. Multiply the j = 3 term by 4.
5.3333
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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