Advertisements
Advertisements
प्रश्न
if `y = sin^(-1) (6xsqrt(1-9x^2))`, `1/(3sqrt2) < x < 1/(3sqrt2)` then find `(dy)/(dx)`
Advertisements
उत्तर
`y = sin^(-1) (6x sqrt(1-9x^2)), -1/(3sqrt2) < x < 1/(3sqrt2)`
`=> y = sin^(-1) (2 xx 3x xx sqrt(1-(3x)^2))`
Putting 3x = sinθ, we have
`y = sin^(-1) (2sin theta sqrt(1- sin^2 theta))`
⇒ y = sin−1 (2sinθ cosθ)
⇒ y = sin−1(sin2θ)
⇒ y = 2θ
`[-1/(3sqrt2) < (sin theta)/3 < 1/(3sqrt2) => - 1/sqrt2 < sin theta < 1/sqrt2 => - pi/4 < theta < pi/4 => -pi/4 < 2theta < pi/2]`
`:. y = 2sin^(-1) 3x`
Differentiating both sides w.r.t x, we get
`(dy)/(dx) = 2 xx 1/(sqrt(1-(3x)^2)) xx 3`
`=> (dy)/dx = 6/sqrt(1- 9x^2)`
APPEARS IN
संबंधित प्रश्न
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find the particular solution of the differential equation `(1+x^2)dy/dx=(e^(mtan^-1 x)-y)` , give that y=1 when x=0.
Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.
Find a particular solution of the differential equation`(x + 1) dy/dx = 2e^(-y) - 1`, given that y = 0 when x = 0.
If y = etan x+ (log x)tan x then find dy/dx
Find `(dy)/(dx)` at x = 1, y = `pi/4` if `sin^2 y + cos xy = K`
Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
The solution of x2 + y2 \[\frac{dy}{dx}\]= 4, is
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
\[\frac{dy}{dx} - y \tan x = - 2 \sin x\]
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
Find the particular solution of the differential equation \[\frac{dy}{dx} = - 4x y^2\] given that y = 1, when x = 0.
Find a particular solution of the following differential equation:- x2 dy + (xy + y2) dx = 0; y = 1 when x = 1
Solve the differential equation: `(d"y")/(d"x") - (2"x")/(1+"x"^2) "y" = "x"^2 + 2`
The general solution of the differential equation `"dy"/"dx" + y/x` = 1 is ______.
The general solution of the differential equation x(1 + y2)dx + y(1 + x2)dy = 0 is (1 + x2)(1 + y2) = k.
x + y = tan–1y is a solution of the differential equation `y^2 "dy"/"dx" + y^2 + 1` = 0.
Solve the differential equation dy = cosx(2 – y cosecx) dx given that y = 2 when x = `pi/2`
Find the general solution of (1 + tany)(dx – dy) + 2xdy = 0.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
General solution of `("d"y)/("d"x) + ytanx = secx` is ______.
Solution of the differential equation `("d"y)/("d"x) + y/x` = sec x is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.
Solve the differential equation:
`(xdy - ydx) ysin(y/x) = (ydx + xdy) xcos(y/x)`.
Find the particular solution satisfying the condition that y = π when x = 1.
