`y = x e ^(-kx)` Find the derivative of the function.

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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = x^n ; then dy/dx = n*x6(n-1) ; where n = real number

2) if y = e^(ax) ; then ; dy/dx = a*e^(ax)

3) If y = u*v ; where u & v are both functions of 'x' ; then

dy/dx = y' = u*(dv/dx) + v*(du/dx)

Now, 

Given y = x*e^(-kx)

thus, y' = dy/dx = -[(kx)*e^(-kx)] + {e^(-kx)}

or, dy/dx = y' = {e^(-kx)}*{1 - kx}