Find the second derivative of the function. f(x) = 4x^-2 - 3x^-4 (x) = ______

Find First Derivative: First, find the first derivative of the function f(x) = 4x^-2 - 3x^-4. Using the power rule for derivatives, d/dx[x^n] = n*x^(n-1), we calculate: f'(x) = 4*(-2)*x^(-2-1) - 3*(-4)*x^(-4-1) = -8x^-3 + 12x^-5Calculate First Derivative: Next, find the second derivative of the function using the first derivative f'(x) = -8x^-3 + 12x^-5. Again applying the power rule: f''(x) = -8*(-3)*x^(-3-1) + 12*(-5)*x^(-5-1) = 24x^-4 - 60x^-6

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Find the second derivative of the function. $\newline$ $f(x) = 4x^{-2} - 3x^{-4}$ $\newline$ $f''(x) =$ ______

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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) = 4x^{-2} - 3x^{-4}

\newline

f''(x) =

______

Find First Derivative: First, find the first derivative of the function $f(x) = 4x^{-2} - 3x^{-4}$ . $\newline$ Using the power rule for derivatives, $\frac{d}{dx}[x^n] = n\cdot x^{(n-1)}$ , we calculate: $\newline$ $f'(x) = 4\cdot(-2)\cdot x^{(-2-1)} - 3\cdot(-4)\cdot x^{(-4-1)}$ $\newline$ = $-8x^{-3} + 12x^{-5}$
Calculate First Derivative: Next, find the second derivative of the function using the first derivative $f'(x) = -8x^{-3} + 12x^{-5}$ . $\newline$ Again applying the power rule: $\newline$ $f''(x) = -8(-3)x^{(-3-1)} + 12(-5)x^{(-5-1)}$ $\newline$ = $24x^{-4} - 60x^{-6}$