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 is \( \frac{d}{dx}(x^{n})=nx^{n - 1} \). For \( y = ax^{n} \), the derivative \( y^\prime=a\times n\times x^{n-1} \). Here \( a = 10 \) and \( n=-2 \). So \( f^\prime(x)=10\times(-2)x^{-2 - 1}\).

Step3: Simplify the expression

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

Answer:

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