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How do you use the chain rule to differentiate #y=3(5x+5)^5#?

Answer 1

Luke Alvarez

Given -

#y=3(5x+5)^5#

#dy/dx=3*5(5x+5)^4(5)#

#dy/dx=75(5x+5)^4#

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Answer 2

Charles Anctil

To differentiate ( y = 3(5x + 5)^5 ) using the chain rule:

Identify the outer function: ( u = 3u^5 )
Identify the inner function: ( v = 5x + 5 )
Differentiate the outer function with respect to its variable: ( \frac{du}{dv} = 15u^4 )
Differentiate the inner function with respect to its variable: ( \frac{dv}{dx} = 5 )
Apply the chain rule: ( \frac{dy}{dx} = \frac{du}{dv} \cdot \frac{dv}{dx} )
Substitute the derivatives: ( \frac{dy}{dx} = 15(5x + 5)^4 \cdot 5 )
Simplify: ( \frac{dy}{dx} = 75(5x + 5)^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.