How do you use the chain rule to differentiate #y=7/(2x+7)^2#?
This said, we have:
So its derivative is:
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To differentiate ( y = \frac{7}{(2x + 7)^2} ) using the chain rule, follow these steps:

Identify the outer function ( f(u) ) and the inner function ( u(x) ).
 The outer function is ( f(u) = u^2 ).
 The inner function is ( u(x) = 2x + 7 ).

Compute the derivative of the outer function with respect to ( u ), denoted as ( f'(u) ), and the derivative of the inner function with respect to ( x ), denoted as ( u'(x) ).
 ( f'(u) = 2u )
 ( u'(x) = 2 )

Substitute the inner function into the derivative of the outer function:
 ( \frac{d}{dx} [f(u)] = f'(u) \cdot u'(x) = 2u \cdot 2 )

Substitute the inner function ( u(x) = 2x + 7 ) back into the result:
 ( \frac{d}{dx} [f(u)] = 2(2x + 7) )

Simplify the expression:
 ( \frac{d}{dx} [f(u)] = 4x + 14 )
Therefore, the derivative of ( y = \frac{7}{(2x + 7)^2} ) with respect to ( x ) is ( \frac{d}{dx} [y] = 4x + 14 ).
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When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
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