How do you differentiate #f(x)=1/sqrt(1x)# using the chain rule?
Rewrite using negative exponents:
Then, applying the Power Rule in conjunction with the Chain Rule,
Rewriting in radical form:
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To differentiate ( f(x) = \frac{1}{\sqrt{1x}} ) using the chain rule, follow these steps:

Identify the outer function and the inner function. In this case, the outer function is ( \frac{1}{\sqrt{x}} ) and the inner function is ( 1x ).

Differentiate the outer function with respect to its variable, treating the inner function as if it were a simple variable. The derivative of ( \frac{1}{\sqrt{x}} ) is ( \frac{1}{2}x^{3/2} ).

Multiply the result from step 2 by the derivative of the inner function with respect to its variable. The derivative of ( 1x ) is ( 1 ).

Combine the results to get the derivative of the entire function. So, the derivative of ( f(x) = \frac{1}{\sqrt{1x}} ) is ( \frac{1}{2}(1x)^{3/2} ).
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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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