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

Answer 1

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

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 #

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Answer 2

Isaiah Allen

To differentiate ( f(x) = (2x - 3)^{-2} ), you would use the chain rule. The derivative is ( f'(x) = -4(2x - 3)^{-3} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.