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Question: If xe^(xy) – y = sin^2x, then find dy/dx at x=0.

Question:
  • If xe^(xy) – y = sin^2x, then find dy/dx at x=0.

Grade:11

2 Answers

Vikas TU
14149 Points
7 years ago
Given eqn.  xe^(xy) – y = sin^2x,
Differentiate y  w.r.t.   x as:

(1)e^(xy) + xe^(xy)*[1.y + xdy/dx] – dy/dx = sin2x
collect dy/dx,

put x = 0:
  dy/dx =  1 is the answer.
Praneet Debnath
33 Points
7 years ago
 
xe^xy – y = sin^2x
 
∴ y = xe^xy – sin^2x

Differention both sides w.r.t  x:

   dy/dx = (1).(e^xy) + (x).(ye^xy) – 2.sinx.cosx
∴ dy/dx = e^xy + xy.e^xy – 2.sinx.cosx
 
NOTE: Differentiate xe^xy by using product rule where u=x and v=e^xy.
 
Substituting x = 0:
∴ dy/dx = e^0 + 0.(ye^xy) – 2.sin0.cos0
∴ dy/dx = 1 + 0 – 0
∴ dy/dx = 1
 
Hope this helps everyone...!!

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