Questions: If f(x) = 1/x^2, find f'(5)

Transcript text: If $f(x)=\frac{1}{x^{2}}$, find $f^{\prime}(5)$

Solution

Solution Steps

Step 1: Finding the First Derivative

Given the function $f(x) = \frac{1}{x^{2}}$, the first derivative $f^{\prime}(x)$ is calculated using the differentiation rules applicable to its terms. Thus, $f^{\prime}(x) = - \frac{2}{x^{3}}$.

Step 2: Finding the Second Derivative

Applying the differentiation rules again to $f^{\prime}(x)$, the second derivative $f^{\prime \prime}(x)$ is found. Thus, $f^{\prime \prime}(x) = \frac{6}{x^{4}}$.

Final Answer:

The first derivative of $f(x)$ is $f^{\prime}(x) = - \frac{2}{x^{3}}$ and the second derivative is $f^{\prime \prime}(x) = \frac{6}{x^{4}}$.

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