Find the second derivative of the function. f(x) = 4/x^3 + 8 (x) = ______

Find First Derivative: First, find the first derivative of f(x). Using the power rule, the derivative of 4/x^3 is -12/x^4 (since the derivative of x^n is n*x^(n-1) and here n = -3). The derivative of a constant (8) is 0. Calculation: f'(x) = -12/x^4 + 0Calculate First Derivative: Next, find the second derivative of f(x). Again using the power rule, the derivative of -12/x^4 is 48/x^5. Calculation: f''(x) = 48/x^5

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Find the second derivative of the function. $\newline$ $f(x) = \frac{4}{x^3} + 8$ $\newline$ $f''(x) =$ ______

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Calculus

Find second derivatives of trigonometric, exponential, and logarithmic functions

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Q. Find the second derivative of the function.

\newline

f(x) = \frac{4}{x^3} + 8

\newline

f''(x) =

______

Find First Derivative: First, find the first derivative of $f(x)$ . Using the power rule, the derivative of $\frac{4}{x^3}$ is $-\frac{12}{x^4}$ (since the derivative of $x^n$ is $n*x^{(n-1)}$ and here $n = -3$ ). The derivative of a constant ( $8$ ) is $0$ . $\newline$ Calculation: $f'(x) = -\frac{12}{x^4} + 0$
Calculate First Derivative: Next, find the second derivative of $f(x)$ . Again using the power rule, the derivative of $-12/x^4$ is $48/x^5$ . $\newline$ Calculation: $f''(x) = 48/x^5$