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How do you differentiate #f(x) = (5x-4 )^(2) # using the chain rule?

Answer 1

Aurora Alvarado

#f'(x)=10(5x-4)#

#f(x)=(5x-4)^2#

Chain Rule: #f'(x)=f(g(x))g'(x)# here #f(x)=x^2# and #g(x)=5x-4#

#f'(x)=2(5x-4)^(2-1)(5-0)# #f'(x)=10(5x-4)#

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Answer 2

Elijah Abram

To differentiate ( f(x) = (5x - 4)^2 ) using the chain rule, follow these steps:

Identify the outer function: ( u = (5x - 4) ).
Identify the inner function: ( v = u^2 ).
Differentiate the outer function with respect to its variable: ( \frac{du}{dx} = 5 ).
Differentiate the inner function with respect to its variable: ( \frac{dv}{du} = 2u ).
Apply the chain rule: ( \frac{dv}{dx} = \frac{dv}{du} \cdot \frac{du}{dx} ).
Substitute the values: ( \frac{dv}{dx} = 2(5x - 4) \cdot 5 ).
Simplify: ( \frac{dv}{dx} = 10(5x - 4) ).

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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.