Let where is a positive integer

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

f(x)=x^{n}

where

n

is a positive integer. (i) Expand

(x+h)^{n}

up to the term containing

h^{2}

. (ii) Using your expansion, establish a general expression for

f'(x)

. (iii) Using the result of part (ii), find the slope of the tangent to the curve

y=x^{4}

x=\dfrac12