DifferentiationHard

Question

If 2x = y1/5 + y-1/5, then (x2 - 1) equals to

Options

A.5y
B.25 y
C.25 y2
D.y + 25

Solution

(y1/5 + y-1/5)2 = (y1/5 - y -1/5)2 + 4
Then    y1/5   - y - 1/5 = 2    ... (1)
Given    y1/5 + y -1/5 = 2x            ... (2)
From (1) & (2)
y = (x + )5
Differentiating both sides w.r.t. x, we get

or  (x2 - 1) = 25y2
Again differentiating w.r.t. x,
2x + 2(x2 - 1) = 50 y
Dividing by 2on both sides
x + (x2 - 1) = 25y 

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