Advertisements
Advertisements
प्रश्न
Trigonometric and inverse-trigonometric functions are differentiable in their respective domain.
पर्याय
True
False
उत्तर
This statement is True.
APPEARS IN
संबंधित प्रश्न
If `sec((x+y)/(x-y))=a^2. " then " (d^2y)/dx^2=........`
(a) y
(b) x
(c) y/x
(d) 0
If `y=sin^-1(3x)+sec^-1(1/(3x)), ` find dy/dx
Differentiate `tan^(-1)(sqrt(1-x^2)/x)` with respect to `cos^(-1)(2xsqrt(1-x^2))` ,when `x!=0`
Find : ` d/dx cos^−1 ((x−x^(−1))/(x+x^(−1)))`
Find the derivative of the following function f(x) w.r.t. x, at x = 1 :
`f(x)=cos^-1[sin sqrt((1+x)/2)]+x^x`
if `y = sin^(-1)[(6x-4sqrt(1-4x^2))/5]` Find `dy/dx `.
If `y=tan^(−1) ((sqrt(1+x^2)+sqrt(1−x^2))/(sqrt(1+x^2)−sqrt(1−x^2)))` , x2≤1, then find dy/dx.
Find `dy/dx` in the following:
`y = cos^(-1) ((1-x^2)/(1+x^2)), 0 < x < 1`
Find `dy/dx` in the following:
`y = sin^(-1) ((1-x^2)/(1+x^2)), 0 < x < 1`
Find `dx/dy` in the following:
`y = cos^(-1) ((2x)/(1+x^2)), -1 < x < 1`
Find `dy/dx` in the following:
`y = sec^(-1) (1/(2x^2 - 1)), 0 < x < 1/sqrt2`
If `sqrt(1-x^2) + sqrt(1- y^2)` = a(x − y), show that dy/dx = `sqrt((1-y^2)/(1-x^2))`
if `x = tan(1/a log y)`, prove that `(1+x^2) (d^2y)/(dx^2) + (2x + a) (dy)/(dx) = 0`
Find \[\frac{dy}{dx}\] at \[t = \frac{2\pi}{3}\] when x = 10 (t – sin t) and y = 12 (1 – cos t).
If y = (sec-1 x )2 , x > 0, show that
`x^2 (x^2 - 1) (d^2 y)/(dx^2) + (2x^3 - x ) dy/dx -2 = 0`
If y = cos (sin x), show that: `("d"^2"y")/("dx"^2) + "tan x" "dy"/"dx" + "y" "cos"^2"x" = 0`
If `log (x^2 + y^2) = 2 tan^-1 (y/x)`, show that `(dy)/(dx) = (x + y)/(x - y)`
If `"y" = (sin^-1 "x")^2, "prove that" (1 - "x"^2) (d^2"y")/(d"x"^2) - "x" (d"y")/(d"x") - 2 = 0`.
`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` is equal to ____________.
`lim_("x"-> 0) ("cosec x - cot x")/"x"` is equal to ____________.
`"d"/"dx" {"cosec"^-1 ((1 + "x"^2)/(2"x"))}` is equal to ____________.
If `"y = sin"^-1 ((sqrt"x" - 1)/(sqrt"x" + 1)) + "sec"^-1 ((sqrt"x" + 1)/(sqrt"x" - 1)), "x" > 0, "then" "dy"/"dx"` is ____________.
The derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `cos^-1 [(1 - x^2)/(1 + x^2)]` is equal to
