## Rules of Differentiation

Rule 1 Derivative of a constant function

Rule 2 Derivative of a linear function:

If f(x) - m x 4- h. with m and b constants, then fix) - m

Rule 3 Derivative of a power function:

Rule 4 Derivative of the constant multiple of a function

Rule 5 Derivative of the sum or difference of a pair of functions Figure 5.18 Consiant function fix | = c has a zero slope

If hix) = g(x) + /(a), then h'ix) = g'ix) + fix), while ifh(x) = g(x) -fix), then h'(x) = g'(jr) - f'{x).

Rule 6 Derivative of the sum of an arbitrary but finite number of functions:

Rule 7 Derivative of the product of two functions:

lfh{x) = f{x)g(x). then h'(x) = f'(x)g(x) + f{x)g'(x).

Rule 8 Derivative of the quotient of two functions:

Rule 9 Derivative of a function of a function—the chain rule:

If y - fin) and u = g(x) so that y = /<gU)) = h(x), then h'(x) = f'iu)g'(x) or dy dy du dx du dx

Rule 10 Derivative of the inverse of a function:

If y = fix) has the inverse function x = giy). that is, if giy) - J ~1 (v) and fix) £ 0. then dx ) , I ,

— = —— or g iy) = —— where y = J ix) dy dy/dx fix)

Rule 11 Derivative of the exponential function: If y = e\ then dy/dx = e*. Rule 12 Derivative of the logarithmic function: Ify = In a, then dy/dx = \/x.