derivative of 5/(2x^2) — step-by-step solution

⚠ 2x is read as the product 2*x: for a power, write 2^x

To ease differentiation, the expression

\frac{5}{2 x^{2}}

is turned into

\frac{5}{2} \cdot x^{-2}

Let's perform the differentiation:

\frac{d}{d x} (\frac{5}{2} \cdot x^{-2})

Apply the differentiation rule:

\frac{d}{d x} (f^{n}) = n \cdot \frac{d}{d x} (f) \cdot f^{(n - 1)}

with f =

x

\frac{5}{2} \cdot (-2 x^{-3})

5 \cdot (-1) \cdot x^{-3}

-5 x^{-3}

▶Derivative:

- \frac{5}{x^{3}}