How do you differentiate #f(x)=sqrtcos(74x) # using the chain rule?
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To differentiate ( f(x) = \sqrt{\cos(7  4x)} ) using the chain rule, follow these steps:

Identify the outer function and the inner function.
 Outer function: ( \sqrt{x} )
 Inner function: ( \cos(7  4x) )

Find the derivative of the outer function with respect to its argument.
 Derivative of ( \sqrt{x} ) is ( \frac{1}{2\sqrt{x}} ).

Find the derivative of the inner function with respect to ( x ).
 Derivative of ( \cos(7  4x) ) is ( \sin(7  4x) \cdot (4) = 4\sin(7  4x) ).

Multiply the derivatives obtained in steps 2 and 3.
 ( \frac{1}{2\sqrt{\cos(7  4x)}} \cdot 4\sin(7  4x) )

Simplify the expression if possible.
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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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