Question

The (1071729)^th derivative of f(x) = (x^6 + x^4 + x^2) cosh(x) at x = 0 is given by

(a) 0

(b) 1071

(c) 1729

(d) ∞

This question was addressed to me in unit test.

This intriguing question comes from Leibniz Rule in portion Differential Calculus of Engineering Mathematics

Answer 1

The correct choice is (a) 0

Explanation: Expanding cosh(x) into a Taylor series we have

cosh(x)=\(\frac{1}{1!}+\frac{x^2}{2!}+\frac{x^4}{4!}…\infty\)

Observe again, that the derivative in question is odd, and hence, only the odd powered terms contribute to the derivative at x = 0

Also note that, there are no odd powered terms and hence we can conclude that

The (1071729)^th derivative must be 0.