Maths (differentiation)

Note that: d/dx (xn) = nxn-1 (Power rule)

while in differentiation, the coefficient of the term can be taken out.

i. f(x) = 2x

df(x)/dx = 2dx/dx = 2

ii. f(x) = x

df(x)/dx = dx/dx = 1

iii.f(x) = 2x2

df(x)/dx = d(2x2)/dx

= 2d(x2)/dx

= 2(2x)

= 4x

iv. f(x) = x2 + 1

df(x)/dx = d(x2 + 1)/dx = 2x

v. f(x) = x2 + 2x

df(x)/dx = d(x2 + 2x)/dx = d(x2)/dx + 2dx/dx = 2x + 2