Consider the function .

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the function

g(x)=4x^{3}-\dfrac{6}{x}+5\sin x-2\cos x

. (i) Find

g'(x)

and simplify each term. (ii) Show that

g'(x)=12x^{2}+\dfrac{6}{x^{2}}+5\cos x+2\sin x

. (iii) Using your result from part (ii), calculate

g'(\dfrac{\pi}{2})

exactly.