# How do you find the derivative using limits of #f(x)=-5x#?

Please see the explanation.

The x terms cancel

Let the limit go to zero:

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To find the derivative of ( f(x) = -5x ), you can use the definition of the derivative, which involves taking the limit of the difference quotient as the interval approaches zero. The derivative of ( f(x) ), denoted as ( f'(x) ) or ( \frac{df}{dx} ), is equal to the limit as ( h ) approaches zero of ( \frac{f(x+h) - f(x)}{h} ). By substituting the function ( f(x) = -5x ) into this formula, you can find the derivative.

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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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