Question:
(a) Differentiate $ \left( \frac{5x}{x^5} \right)$ with respect to $x$.
(a) Differentiate $ \left( \frac{5x}{x^5} \right)$ with respect to $x$.
Updated On: Mar 7, 2026
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Solution and Explanation
To differentiate \(\frac{5x}{x^5}\) with respect to \(x\), simplify the expression first:
\(\frac{5x}{x^5} = 5x \cdot x^{-5} = 5x^{1-5} = 5x^{-4}\)
Now, differentiate \(5x^{-4}\) using the power rule (\(\frac{d}{dx}[x^n] = n x^{n-1}\)):
\(\frac{d}{dx}[5x^{-4}] = 5 \cdot (-4) x^{-4-1} = -20x^{-5}\)
So, the derivative is \(-20x^{-5}\), or equivalently, \(\frac{-20}{x^5}\).
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