# How do you use the chain rule to differentiate #y=(4x+5)^5#?

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To differentiate ( y = (4x + 5)^5 ) using the chain rule, you would first identify the inner function as ( u = 4x + 5 ). Then, you would differentiate ( u ) with respect to ( x ) to get ( \frac{du}{dx} = 4 ). Next, you would differentiate the outer function ( y = u^5 ) with respect to ( u ), resulting in ( \frac{dy}{du} = 5u^4 ). Finally, applying the chain rule, you multiply ( \frac{dy}{du} ) and ( \frac{du}{dx} ) to obtain the derivative of ( y ) with respect to ( x ), which is ( \frac{dy}{dx} = 5(4x + 5)^4 \cdot 4 ).

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