If y=√x+1/√x show that 2x d y /dx +y =2√x
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We have,
y = √x + 1/√x
Therefore,
dy/dx=d/dx(√x)+d/dx(1/√x)
= 1/(2√x) – 1/(2x√x)
Or,
2x dy/dx = √x – 1/√x
Or,
2x dy/dx + y=√x – 1/√x + y
=√x – 1/√x + √x + 1/√x
= 2√x.
y = √x + 1/√x
Therefore,
dy/dx=d/dx(√x)+d/dx(1/√x)
= 1/(2√x) – 1/(2x√x)
Or,
2x dy/dx = √x – 1/√x
Or,
2x dy/dx + y=√x – 1/√x + y
=√x – 1/√x + √x + 1/√x
= 2√x.
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