Misalkan u(x),v(x),w(x),h(x),dan g(x) adalah fungsi yang dapat diturunkan dengan menggunakan konsep turunan sebagai limit fungsi tentukanlah turunan sari fungsi

a. f(x) = y = (2x + 1)²

misal :
u = 2x + 1, du/dx = 2
y = u², dy/du = 2u = 2(2x + 1) = 4x + 2

y' = dy/dx = dy/du . du/dx = (4x + 2). 2
                                         = 8x + 4

jadi y ' = f'(x) = 8x + 4

b. f(x) = y =  (x² - x + 1)²
misal :
u = x² - x + 1............. du/dx = 2x - 1
y = u²........................ dy/du = 2u = 2(x² - x + 1) = 2x² - 2x + 2

y' = dy/du . du/dx = (2x² - 2x + 2) . (2x - 1)
jadi f'(x) = (2x² - 2x + 2)(2x - 1)

c. f(x) = u(x) v(x) w(x)
ln f(x) = ln u(x) v(x) w(x)
ln f(x) = ln u(x) + ln v(x) + ln w(x)
f'(x)/f(x) = u'(x)/u(x) + v'(x)/v(x) + w'(x)/w(x)
f'(x) = {u'(x) / u(x) + v'(x) / v(x) + w'(x) / w(x)} f(x)
f'(x) = {(u'(x) v(x) w(x) + v'(x) u(x) w(x) + w'(x) u(x) v(x))/ u(x) v(x) w(x)} f(x)
f'(x) = {(u'(x) v(x) w(x) + v'(x) u(x) w(x) + w'(x) u(x) v(x))/ f(x)} f(x)
f'(x) = u'(x) v(x) w(x) + v'(x) u(x) w(x) + w'(x) u(x) v(x)