Question

a. find the derivative of the following.
i. $f(x)=\frac{10}{x^{2}}$

Explanation:

Step1: Rewrite the function

Rewrite \( f(x)=\frac{10}{x^{2}} \) as \( f(x) = 10x^{-2} \).

Step2: Apply the power rule

The power rule for differentiation is \( \frac{d}{dx}(x^{n})=nx^{n - 1} \).
For \( y = ax^{n} \), where \( a = 10 \) and \( n=-2 \), the derivative \( f^{\prime}(x)=a\times n\times x^{n - 1} \).
Substitute \( a = 10 \) and \( n=-2 \) into the formula:
\( f^{\prime}(x)=10\times(-2)x^{-2-1}\)

Step3: Simplify the expression

\( f^{\prime}(x)=-20x^{-3}=-\frac{20}{x^{3}} \)

Answer:

\( f^{\prime}(x)=-\frac{20}{x^{3}} \)