Advertisements
Advertisements
प्रश्न
If `y=sin^-1(3x)+sec^-1(1/(3x)), ` find dy/dx
उत्तर
`y=sin^-1(3x)+sec^-1(1/(3x))`
`dy/dx=d/dxsin^-1(3x)+d/dxsec^-1(1/(3x))`
`dy/dx=3/sqrt(1 -(3x)^2) + ((-1)/(3x^2))/(1/(3x)sqrt((1/(3x)^2-1)))`
`dy/dx= 3/sqrt(1-9x^2) - 1/("X" sqrt((1-9x^2))/(3|x|))`
`= 3/sqrt(1-9x^2) - (3|x|)/("X" sqrt(1-9x^2))`
`= 3/(sqrt (1 -9x^2)) (1 - |X|/X)`
= 0 X > 0
= `6/sqrt(1-9"x"^2)` X < 0
APPEARS IN
संबंधित प्रश्न
Differentiate `cos^-1((3cosx-2sinx)/sqrt13)` w. r. t. x.
If `sec((x+y)/(x-y))=a^2. " then " (d^2y)/dx^2=........`
(a) y
(b) x
(c) y/x
(d) 0
Differentiate `tan^(-1)(sqrt(1-x^2)/x)` with respect to `cos^(-1)(2xsqrt(1-x^2))` ,when `x!=0`
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 `.
Find `dy/dx` in the following:
`y = tan^(-1) ((3x -x^3)/(1 - 3x^2)), - 1/sqrt3 < x < 1/sqrt3`
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 = sin^(-1)(2xsqrt(1-x^2)), -1/sqrt2 < x < 1/sqrt2`
Find `dy/dx` in the following:
`y = sec^(-1) (1/(2x^2 - 1)), 0 < x < 1/sqrt2`
Differentiate w.r.t. x the function:
`cot^(-1) [(sqrt(1+sinx) + sqrt(1-sinx))/(sqrt(1+sinx) - sqrt(1-sinx))]`, ` 0 < x < pi/2`
Differentiate w.r.t. x the function:
`(sin x - cos x)^(sin x - cos x), pi/4 < x < (3pi)/4`
If `sqrt(1-x^2) + sqrt(1- y^2)` = a(x − y), show that dy/dx = `sqrt((1-y^2)/(1-x^2))`
Find the approximate value of tan−1 (1.001).
Differentiate `tan^(-1) ((1+cosx)/(sin x))` with respect to x
if `x = tan(1/a log y)`, prove that `(1+x^2) (d^2y)/(dx^2) + (2x + a) (dy)/(dx) = 0`
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 `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`.
The function f(x) = cot x is discontinuous on the set ______.
`lim_("h" -> 0) (1/("h"^2 sqrt(8 + "h")) - 1/(2"h"))` 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 x with respect to log x is ____________.
Let f(x) = `cos(2tan^-1sin(cot^-1sqrt((1 - x)/x))), 0 < x < 1`. Then ______.
