How do you differentiate #f(x) = (2x-3) ^ -2#?

1 Answer
Apr 24, 2016

Answer:

# (-4)/(2x-3)^3 #

Explanation:

differentiate using the #color(blue)" chain rule " #

# d/dx [f(g(x)) ] = f'(g(x)) . g'(x) #
#"----------------------------------------------"#

f(g(x)) #=(2x-3)^(-2) rArr f'(g(x)) = -2(2x-3)^(-3) #

and g(x) = 2x - 3 → g'(x) = 2
#"----------------------------------------------"#
Substitute these values into the derivative

#rArr f'(x) = -2(2x-3)^(-3)xx2 = (-4)/(2x-3)^3 #