Mathematics

Problem

Values of the functions

f

and

g

and their first derivatives are given in the tables below: x g(x) g'(x) 0 2 -1 1 4 0 2 5 3 3 7 -2 u f(u) f'(u) 2 -3 6 4 1 -2 5 -1 -4 7 0 5 Let

y = f\bigl(g(x)\bigr)

. Calculate

\dfrac{dy}{dx}

x = 2