# How do you find the derivative of #f(x)=(6-5x)^-1#?

Use the chain rule, where if

then

then

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To find the derivative of ( f(x) = (6 - 5x)^{-1} ), you can use the chain rule. First, rewrite the function as ( f(x) = (6 - 5x)^{-1} = (6 - 5x)^{-1} ). Then, differentiate with respect to ( x ) using the chain rule, which states that the derivative of ( f(g(x)) ) is ( f'(g(x)) \cdot g'(x) ). In this case, ( f(g(x)) = g(x)^{-1} ), so the derivative is ( -1 \cdot (6 - 5x)^{-2} \cdot (-5) = \frac{5}{(6 - 5x)^2} ). Therefore, the derivative of ( f(x) ) is ( \frac{5}{(6 - 5x)^2} ).

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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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