What is the derivative of 2^(1-x)

What is the derivative of 2^(1-x)?
I need to figure out the slope of the tangent line at x=2

d/dx[2^(1-x)] = 2^(1-x)*ln(1/2)

Slope of the tangent line at x = 2 : 1/2*ln(1/2)

y = 2^(1-x)

ln y = (1-x) ln (2)

y'/y = - ln 2

y' = - y ln 2

y ' = -2^(1-x) ln (2)

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at x = 2

y ' = -2^(-1) ln(2)

y ' = - 0.5 ln (2)

y = 2^(1 - x)

log y = ( 1 - x ) log 2

(1/y) dy/dx = - log 2

dy/dx = - y log 2

dy/dx = - 2^(1 - x) log 2

dy/dx = - 2^(-1) log 2

dy/dx = - log 2 / 2