x/2 is the same as (1/2) times x. Thus, you can use the formula for a constant factor.
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The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
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Well, isn't that a happy little question! To find the derivative of x divided by y, you can use the quotient rule. The derivative will be (y * d/dx(x) - x * d/dx(y)) / (y^2). Just remember, there are no mistakes, just happy little accidents in math!
e^(-2x) * -2 The derivative of e^F(x) is e^F(x) times the derivative of F(x)
Your expression simplifies to just x^2 {with the restriction that x > 0}. The derivative of x^2 is 2*x