Question

Leibniz theorem is applicable if n is a

(a) Rational Number

(b) Negative Integer

(c) Positive Integer

(d) Decimal Number

I had been asked this question at a job interview.

This interesting question is from Leibniz Rule in chapter Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (c) Positive Integer

To explain: Leibniz rule is

\(\frac{d^n}{dx^n}(uv)\)

\(= n_{C_0} u_n v+ n_{C_1} u_{n-1} v_1+ n_{C_2} u_{n-2} v_2+…+ n_{C_r} u_{n-r} v_r+…+ n_{C_n} u_0 v_n\)

For all n > 0, i.e n should be positive

Hence Leibniz theorem gives nth derivative of multiplication of two functions u and v if n is a positive integer.