Find (d)/(dx)(-4x^(4)-x^(-2)-5)

Question

Find  (d)/(dx)(-4x^(4)-x^(-2)-5)

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Apply Derivative Operator: Apply the derivative operator to each term in the function separately. We have the function f(x) = -4x^(4) - x^(-2) - 5, and we want to find its derivative f'(x). We can use the linearity of the derivative to take the derivative of each term separately.Derivative of -4x^(4): Find the derivative of the first term -4x^(4). Using the power rule for derivatives, (d/dx)(x^n) = nx^(n-1), we find the derivative of -4x^(4). (d/dx)(-4x^(4)) = -4 * 4x^(4-1) = -16x^(3).Derivative of -x^(-2): Find the derivative of the second term -x^(-2). Again using the power rule, we find the derivative of -x^(-2). (d/dx)(-x^(-2)) = -(-2)x^(-2-1) = 2x^(-3).Derivative of Constant Term: Find the derivative of the constant term -5. The derivative of a constant is 0. (d/dx)(-5) = 0.Combine Derivatives: Combine the derivatives of all terms to get the final derivative of the function. f'(x) = (-16x^(3)) + (2x^(-3)) + (0).Simplify Final Derivative: Simplify the final derivative expression if necessary. In this case, the expression is already simplified. f'(x) = -16x^(3) + 2x^(-3).

Find $\frac{d}{dx}(-4x^{4}-x^{-2}-5)$

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Find $\frac{d}{dx}(-4x^{4}-x^{-2}-5)$