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if y=xe^x then prove that 1/y dy/dx= 1+1/x prove it prove it plzz plzz plzzz

if y=xe^x then prove that 1/y dy/dx= 1+1/x prove it prove it plzz plzz plzzz

Grade:12

1 Answers

Arun
25763 Points
3 years ago
y = x e^x
Differentiating both the sides with reapect to x
dy/dx = x e^x + e^x
dy/dx = e^x (x+1)
In the RHS mutliply and divide by x
Hence
dy/dx = [x e^x (x+1)]/ x
But 
x e^x = y
Hence
dy/dx = y[1 +(1/x)]
1/y dy/dx = 1 +(1/x)

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