(1/2)x = 2-x = exp (ln 2-x) = exp( -x ln 2). Since d/dx exp(x) = exp(x), we can use the chain rule to find that:
d/dx (1/2)x = -(ln 2) exp(-x ln 2).
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The square root of x = x to the power of a half
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
The first derivative of e to the x power is e to the power of x.
The derivative of ex is ex
2x