Derivative of a negative power function

Apply the power rule to $x^{-1}$: bring down the exponent $-1$ as a coefficient and subtract 1 from it, giving $\frac{d}{dx}[x^{-1}] = -1\cdot x^{-1-1} = -x^{-2}$.

Multiply by the constant 5 using the constant multiple rule: $f'(x) = 5\cdot(-x^{-2}) = -5x^{-2}$. Rewriting with a positive exponent gives $f'(x) = -\dfrac{5}{x^2}$.

The derivative found in part a was negative five over x squared. For any positive value of x, x squared is positive, so negative five divided by a positive number is negative. Therefore the derivative is negative for positive x.