Question

Leibniz rule gives the

(a) Nth derivative of addition of two function

(b) Nth derivative of division of two functions

(c) Nth derivative of multiplication of two functions

(d) Nth derivative of subtraction of two function

I got this question in examination.

My question is taken from Leibniz Rule in section Differential Calculus of Engineering Mathematics

Answer 1

Right option is (c) Nth derivative of multiplication of two functions

Best explanation: Leibniz rule is

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

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

Hence Leibniz theorem gives nth derivative of multiplication of two functions u and v.

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