Derivative of (x^3)-4x/(1/2)x^(-1/2)

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Derivative of (x^3)-4x/(1/2)x^(-1/2): 


(x^3-(x^(-1/2)*((4*x)/(1/2))))'

(x^3)'+(-(x^(-1/2)*((4*x)/(1/2))))'

(-(x^(-1/2)*((4*x)/(1/2))))'+3*x^(3-1)

(x^(-1/2))'*((4*x)/(1/2))+x^(-1/2)*((4*x)/(1/2))'+3*x^2

(-1/2)*x^(-1/2-1)*(x)'*((4*x)/(1/2))+x^(-1/2)*((4*x)/(1/2))'+3*x^2

x^(-1/2)*((4*x)/(1/2))'+3*x^2+(-1/2)*x^(-1/2-1)*1*((4*x)/(1/2))

x^(-1/2)*((4*x)/(1/2))'+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

x^(-1/2)*(((4*x)'*(1/2)-(4*x*(1/2)'))/((1/2)^2))+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

x^(-1/2)*((((4)'*x+4*(x)')*(1/2)-(4*x*(1/2)'))/((1/2)^2))+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

x^(-1/2)*(((0*x+4*(x)')*(1/2)-(4*x*(1/2)'))/((1/2)^2))+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

x^(-1/2)*(((0*x+4*1)*(1/2)-(4*x*(1/2)'))/((1/2)^2))+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

x^(-1/2)*((4*(1/2)-(4*x*(1/2)'))/((1/2)^2))+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

x^(-1/2)*((4*(1/2)-(4*x*0))/((1/2)^2))+3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))

3*x^2-1/2*x^(-3/2)*((4*x)/(1/2))+x^(-1/2)*8

3*x^2-(4*x^(-1/2))

The calculation above is a derivative of the function f (x)

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