If `y=log_(x^(2)+4)(7x^(2)-5x+1)`, then `(dy)/(dx)` is equal to

Options

A. ` log_(e)(x^(2)+ 4).{(14x -5)/(7x^(2) - 5x + 1) - (2xy)/(x^(2) + 4)}`
B. `(1)/(log_(e)(x^(2)+ 4)){(14x -5)/(7x^(2) - 5x + 1) - (2xy)/(x^(2) + 4)}`
C. `log_(e)(7x^(2)+ 5x+1){(2x)/(x^(2) + 4) - ((14x - 5)y)/(7x^(2) + 5x + 1)}`
D. `(1)/log_(e)(7x^(2)+ 5x+1){(2x)/(x^(2) + 4) - ((14x - 5)y)/(7x^(2) + 5x + 1)}`

Answer

B

Explanation

We have ,
` y = log_(x^(2) + 4)(7x^(2) - 5x +1) = (log (7x^(2) - 5x +1))/(log_(e)(x^(2) +4)) = (log_(e) f(x))/(log_(e) g(x))`
`(dy)/(dx) = (log_(e) (g(x)).(f'(x))/(f(x)) - log_(e) f(x).(g'(x))/(g(x)))/((log_(e) g(x))^(2))`
` rArr (dy)/(dx) = (1)/(log_(e) g(x)){(f'(x))/(f(x))- y(g'(x))/(g(x))} `
`rArr (dy)/(dx) = (1)/(log_(e) (x^(2) + 4)){(14 x- 5)/(7x^(2) - 5x + 1)-(2xy)/(x^(2) +4)}`