Let , and let denote the th derivative of . Which of the following statements about…
MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation
Problem
Let f(x)=tanx, and let f(n)(x) denote the nth derivative of f. Which of the following statements about f(n)(0) is correct for all positive integers n?
(a) f(n)(0)=0 when n is even and f(n)(0)=0 when n is odd.
(b) f(n)(0)=0 when n is odd and f(n)(0)=0 when n is even.
(c) f(n)(0)=0 only when n is a multiple of 4.},{
(d) f(n)(0)=0 for every positive integer n.}