Page 16 - Grab Me SPM Add Mathematics Form 4,5

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2.2 The First Derivative
• Differentiation is a process of determining the gradient function of a function y = f(x).
• The gradient function is also known as the first derivative of a function or the derivative function
or the differential coefficient of y with respect to x.
• Techniques of differentiation for an algebraic function:

n
General formula If y = ax where a and n are constants, then dy = nax n – 1
dx
Algebraic sum If y = f(x) ± g(x), then dy = fʹ(x) ± gʹ(x)
and difference dx
(a) If y = f(u) where u = g(x), then dy = dy × du
Chain rule dx du dx
(b) If y = [f(x)] where n is a constant, then dy = n[f(x)] n – 1 fʹ(x)
n
dx
Product rule If y = uv where u = f(x) and v = g(x), then dy = u dv + v du = uvʹ + vuʹ
dx dx dx
v du – u dv
Quotient rule u dy dx dx vuʹ – uvʹ
If y = where u = f(x) and v = g(x), then = 2 =
v dx v v 2

Ch 2_Grab Me SPM AddMaths F5.indd 132 13/05/2022 9:09 AM