Advertisements
Advertisements
प्रश्न
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to ______.
पर्याय
`(4x^3)/(1 - x^4)`
`(-4x)/(1 - x^4)`
`1/(4 - x^4)`
`(-4x^3)/(1 - x^4)`
Advertisements
उत्तर
If y = `log ((1 - x^2)/(1 + x^2))`, then `"dy"/"dx"` is equal to `(-4x)/(1 - x^4)`.
Explanation:
Given that: y = `log ((1 - x^2)/(1 + x^2))`
⇒ y = log(1 – x2) – log(1 + x2) ....`[because log x/y = log x - log y]`
Differentiating both sides w.r.t. x
`"dy"/"dx" = 1/(1 - x^2) * "d"/"dx"(1 - x^2) - 1/(1 + x^2) (1 + x^2)`
= `(-2x)/(1 - x^2) - (2x)/(1 + x^2)`
= `(-2x - 2x^3 - 2x + 2x^3)/((1 - x^2)(1 + x^2))`
= `(-4x)/(1 - x^4)`.
APPEARS IN
संबंधित प्रश्न
Differentiate the function with respect to x.
cos x . cos 2x . cos 3x
Differentiate the function with respect to x.
xx − 2sin x
Find `bb(dy/dx)` for the given function:
xy = `e^((x - y))`
Find the derivative of the function given by f(x) = (1 + x) (1 + x2) (1 + x4) (1 + x8) and hence find f′(1).
If u, v and w are functions of x, then show that `d/dx(u.v.w) = (du)/dx v.w + u. (dv)/dx.w + u.v. (dw)/dx` in two ways-first by repeated application of product rule, second by logarithmic differentiation.
If x = a (cos t + t sin t) and y = a (sin t – t cos t), find `(d^2y)/dx^2`.
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Differentiate
log (1 + x2) w.r.t. tan-1 (x)
Find `(d^2y)/(dx^2)` , if y = log x
Solve the following differential equation: (3xy + y2) dx + (x2 + xy) dy = 0
If `(sin "x")^"y" = "x" + "y", "find" (d"y")/(d"x")`
If xy = ex–y, then show that `"dy"/"dx" = logx/(1 + logx)^2`.
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
Differentiate 3x w.r.t. logx3.
If y = log (log 2x), show that xy2 + y1 (1 + xy1) = 0.
If y = `log[4^(2x)((x^2 + 5)/sqrt(2x^3 - 4))^(3/2)]`, find `("d"y)/("d"x)`
If log5 `((x^4 + "y"^4)/(x^4 - "y"^4))` = 2, show that `("dy")/("d"x) = (12x^3)/(13"y"^2)`
If y = `(sin x)^sin x` , then `"dy"/"dx"` = ?
lf y = `2^(x^(2^(x^(...∞))))`, then x(1 - y logx logy)`dy/dx` = ______
If xy = ex-y, then `"dy"/"dx"` at x = 1 is ______.
`d/dx(x^{sinx})` = ______
`"d"/"dx" [(cos x)^(log x)]` = ______.
`log (x + sqrt(x^2 + "a"))`
If xm . yn = (x + y)m+n, prove that `"dy"/"dx" = y/x`
If `"y" = "e"^(1/2log (1 + "tan"^2"x")), "then" "dy"/"dx"` is equal to ____________.
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
If `log_10 ((x^3 - y^3)/(x^3 + y^3))` = 2 then `dy/dx` = ______.
Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.
Find `dy/dx`, if y = (sin x)tan x – xlog x.
If y = `9^(log_3x)`, find `dy/dx`.
The derivative of log x with respect to `1/x` is ______.
Find the derivative of `y = log x + 1/x` with respect to x.
After differentiating \[\log y=v(x)\cdot\log[u(x)]\], which equation is obtained?
For \[y=x^{\sin x}\], \[x>0\], what equation results after taking logarithm on both sides?
