find the derivative of $f(x)=\\frac{x^{2}}{x^{3}}$.
find the derivative of $f(x)=\\frac{x^{2}}{x^{3}}$.
Answer
Explanation:
Step1: Simplify the function
$$f(x)=\frac{x^{2}}{x^{3}}=x^{2 - 3}=x^{-1}$$
Step2: Apply the power rule
The power rule for differentiation is $\frac{d}{dx}(x^{n})=nx^{n - 1}$. For $n=-1$, we have: $$f^{\prime}(x)=(-1)x^{-1-1}$$
Step3: Simplify the result
$$f^{\prime}(x)=-x^{-2}=-\frac{1}{x^{2}}$$
Answer:
$-\frac{1}{x^{2}}$