(d)/(dx)(-4x^(4//3)-2x^(-3//4)+3)

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Identify Function: Identify the function to differentiate: f(x) = -4x^(4/3) - 2x^(-3/4) + 3. We will use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).Differentiate First Term: Differentiate the first term -4x^(4/3) using the power rule. The derivative of -4x^(4/3) with respect to x is -4 * (4/3) * x^((4/3)-1). Simplify the exponent: (4/3) - 1 = (4/3) - (3/3) = 1/3. So, the derivative of the first term is -4 * (4/3) * x^(1/3).Differentiate Second Term: Differentiate the second term -2x^(-3/4) using the power rule. The derivative of -2x^(-3/4) with respect to x is -2 * (-3/4) * x^((-3/4)-1). Simplify the exponent: (-3/4) - 1 = (-3/4) - (4/4) = -7/4. So, the derivative of the second term is -2 * (-3/4) * x^(-7/4).Differentiate Third Term: Differentiate the third term +3. The derivative of a constant is 0. So, the derivative of the third term is 0.Combine Derivatives: Combine the derivatives of all terms to get the final derivative of the function. The derivative of f(x) is -4 * (4/3) * x^(1/3) + -2 * (-3/4) * x^(-7/4) + 0. Simplify the coefficients: -4 * (4/3) = -16/3 and -2 * (-3/4) = 3/2. So, the final derivative of f(x) is (-16/3)x^(1/3) + (3/2)x^(-7/4).

$\left(\frac{d}{dx}\right)(-4x^{\frac{4}{3}}-2x^{-\frac{3}{4}}+3)$

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$\left(\frac{d}{dx}\right)(-4x^{\frac{4}{3}}-2x^{-\frac{3}{4}}+3)$