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)`
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 following function with respect to x: `(log x)^x+x^(logx)`
if xx+xy+yx=ab, then find `dy/dx`.
Differentiate the function with respect to x.
`x^x - 2^(sin x)`
Find `dy/dx`for the function given in the question:
xy + yx = 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^m y^n = (x + y)^(m + n)`, prove that `(d^2y)/(dx^2)= 0`
If ey ( x +1) = 1, then show that `(d^2 y)/(dx^2) = ((dy)/(dx))^2 .`
Find `(dy)/(dx) , if y = sin ^(-1) [2^(x +1 )/(1+4^x)]`
Find `"dy"/"dx"` if y = xx + 5x
If ey = yx, then show that `"dy"/"dx" = (logy)^2/(log y - 1)`.
If x = log(1 + t2), y = t – tan–1t,show that `"dy"/"dx" = sqrt(e^x - 1)/(2)`.
Find the second order derivatives of the following : x3.logx
Find the nth derivative of the following : log (ax + b)
If y = `25^(log_5sin_x) + 16^(log_4cos_x)` then `("d"y)/("d"x)` = ______.
If y = 5x. x5. xx. 55 , find `("d"y)/("d"x)`
Derivative of loge2 (logx) with respect to x is _______.
If y = tan-1 `((1 - cos 3x)/(sin 3x))`, then `"dy"/"dx"` = ______.
`d/dx(x^{sinx})` = ______
`2^(cos^(2_x)`
`log (x + sqrt(x^2 + "a"))`
`lim_("x" -> -2) sqrt ("x"^2 + 5 - 3)/("x" + 2)` is equal to ____________.
If y = `x^(x^2)`, then `dy/dx` is equal to ______.
Derivative of log (sec θ + tan θ) with respect to sec θ at θ = `π/4` is ______.
The derivative of x2x w.r.t. x is ______.
If y = `9^(log_3x)`, find `dy/dx`.
The derivative of log x with respect to `1/x` is ______.
If xy = yx, then find `dy/dx`
