# How do you differentiate #f(x)=sec(e^(x)-3x ) # using the chain rule?

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To differentiate ( f(x) = \sec(e^x - 3x) ) using the chain rule, follow these steps:

- Identify the outer function as ( \sec(u) ) and the inner function as ( u = e^x - 3x ).
- Differentiate the inner function ( u ) with respect to ( x ) to find ( \frac{du}{dx} ).
- Apply the chain rule: [ \frac{d}{dx}[\sec(u)] = \sec(u) \tan(u) \frac{du}{dx} ]
- Substitute ( u = e^x - 3x ) into the expression.
- Compute ( \frac{du}{dx} ).
- Substitute all values into the chain rule formula to find ( \frac{d}{dx}[f(x)] ).

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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.

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.

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.

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