Mathematics

Problem

While deriving

\dfrac{d}{dx}(x^{n})

for a positive integer

n

using the expression

\dfrac{(x+h)^{n}-x^{n}}{h}

, the term that remains after cancellation of

x^{n}

and division by

h

is ______. Which option correctly identifies the coefficient of

x^{n-1}

in that term? a)

n-1

\dfrac{n(n-1)}{2}

n

n^{2}