Advertisements
Advertisements
प्रश्न
Differentiate the following with respect to x.
`sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
Advertisements
उत्तर
Let y = `sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))`
y = `(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1)))^(1/2)`
Taking logarithm on both sides we get,
log y = `1/2` {[log(x – 1) + log(x – 2)] – [(log(x – 3) + log(x2 + x + 1)]}
log y = `1/2` [log(x – 1) + log(x – 2) – log(x – 3) – log(x2 + x + 1)]
Differentiating with respect to x,
`1/y "dy"/"dx" = 1/2[1/(x - 1) (1 - 0) + 1/(x - 2)(1 - 0) - 1/(x -3)(1 - 0) - 1/(x^2 + x + 1) (2x + 1)]`
`1/y "dy"/"dx" = 1/2[1/(x - 1) + 1/(x - 2) - 1/(x - 3) - (2x + 1)/(x^2 + x + 1)]`
`therefore "dy"/"dx" = 1/2 y [1/(x - 1) + 1/(x - 2) - 1/(x - 3) - (2x + 1)/(x^2 + x + 1)]`
`= 1/2 sqrt(((x - 1)(x - 2))/((x - 3)(x^2 + x + 1))) [1/(x - 1) + 1/(x - 2) - 1/(x - 3) - (2x + 1)/(x^2 + x + 1)]`
APPEARS IN
संबंधित प्रश्न
Differentiate the following with respect to x.
`(sqrtx + 1/sqrtx)^2`
Differentiate the following with respect to x.
`e^x/(1 + x)`
Differentiate the following with respect to x.
`(x^2 + x + 1)/(x^2 - x + 1)`
Differentiate the following with respect to x.
ex sin x
Differentiate the following with respect to x.
cos3 x
Differentiate the following with respect to x.
(ax2 + bx + c)n
If `xsqrt(1 + y) + ysqrt(1 + x)` = 0 and x ≠ y, then prove that `"dy"/"dx" = - 1/(x + 1)^2`
Find y2 for the following function:
x = a cosθ, y = a sinθ
If y = `(x + sqrt(1 + x^2))^m`, then show that (1 + x2) y2 + xy1 – m2y = 0
If y = tan x, then prove that y2 - 2yy1 = 0.
