Use the Reciprocal Rule to determine the derivative of the function $$ f(x)=\frac{1}{1-5 x} $$

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1. Write the function as $$ f(x)=\frac{1}{1-5x} $$.

2. Identify the inner function as $$ g(x)=1-5x $$, so that $$ f(x)=\frac{1}{g(x)} $$.

3. The Reciprocal Rule tells us that for $$ f(x)=\frac{1}{g(x)} $$,
   $$
   f'(x)=-\frac{g'(x)}{(g(x))^2}.
   $$

4. Differentiate $$ g(x)=1-5x $$:
   $$
   g'(x)=-5.
   $$

5. Substitute $$ g(x) $$ and $$ g'(x) $$ into the formula:
   $$
   f'(x)=-\frac{-5}{(1-5x)^2}=\frac{5}{(1-5x)^2}.
   $$

Thus, the derivative of $$ f(x)=\frac{1}{1-5x} $$ is
$$
f'(x)=\frac{5}{(1-5x)^2}.
$$
The derivative of $$ f(x)=\frac{1}{1-5x} $$ is $$ f'(x)=\frac{5}{(1-5x)^2} $$.

Use the Reciprocal Rule to determine the derivative of the function

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