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If 5f(x)+3f(1/x)=x+2 and y=x f(x), then...

If `5f(x)+3f(1/x)=x+2` and `y=x f(x),` then find `dy/dx` at `x=1`.

A

14

B

`7//8`

C

1

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
` 5f(x) + 3f ((1)/(x)) = x + 2 ` …(2)
On replacing x by `1/x`, we get
` 5f((1)/(x)) + 3f (x) = 1/x + 2 ` …(iii)
On multiplying Eq. (i) by 5 and Eq . (ii) by 3 and then on
subtracting , we get
` 16f(x) = 5x - (3)/(x) + 4 `
`rArr xf(x) = (5x^(2) - 3 + 4x )/(16 = y `
` therefore (dy)/(dx) = (10 x + 4)/(16)
`[(dy)/(dx)]_(x =1) = (10 + 4)/(16) = (7)/(8)`
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