Question 1010647
Use the logarithmic differentiation to differentiate the function

y= (x+2)^2/(e^x*sqrt(x^2+16))
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{{{y = (x+2)^2*e^(-x)*(x^2+16)^(-0.5)}}}
Use the product rule:
d/dx(u*v*w) = (du/dx)*v*w + (dv/dx)*u*w + (dw/dx)*u*v
du/dx = 2(x+2)
dv/dx = {{{-e^(-x)}}}
dw/dx = {{{(-1/2)*(x^2+16)^(-1.5)*2x = -x*(x^2+16)^(-1.5)}}}
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The rest is just bookkeeping.