SOLUTION: Use the logarithmic differentiation to differentiate the function y= (x+2)^2/(e^x √(x^2+16))

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Question 1010647: Use the logarithmic differentiation to differentiate the function
y= (x+2)^2/(e^x √(x^2+16))
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use the logarithmic differentiation to differentiate the function
y= (x+2)^2/(e^x*sqrt(x^2+16))
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y+=+%28x%2B2%29%5E2%2Ae%5E%28-x%29%2A%28x%5E2%2B16%29%5E%28-0.5%29
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%5E%28-x%29
dw/dx = %28-1%2F2%29%2A%28x%5E2%2B16%29%5E%28-1.5%29%2A2x+=+-x%2A%28x%5E2%2B16%29%5E%28-1.5%29
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The rest is just bookkeeping.