If x = a (θ - sin θ) and y = a (1 - cos θ), find y_{2} at θ = .

find the derivative of cos root x wrt x from first principle??

Find the intervals in which the function f(x) = sin^4x + cos^4x is increasing or decreasing where the range of x is ( 0, pie/2) .

If y = sin (sin x), prove that

d^{2}y/dx^{2} + (tan x) dy/dx + y cos^{2} x = 0.

If x^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x.

Examine continuity of function f(x) = e^{1/x}-1 / e^{1/x}+1 at x=0

if xy _{+}_{y}x = _{a}b find dy/dx

If x=tan(1/a logy) Show that (1+x^{2})d^{2}y/dx^{2} + (2x-a)dy/dx = 0

if x=a sin2t(1+cos2t) and y=b cos2t(1-cos2t) find dy/dx.

if x=2cost -cos2t and y=2sint -sin2t . find d^{2}y/dx^{2.plzzz help}

Please solve the following problems.

1. Y = Sin(mSin^{-1}x) prove that 1-x^{2}^{ }- xy^{-1} +m^{2}y = 0

2

2. Y = Cosec x + Cot x prove that sin x (d^{2}y ) = y^{2}

dx^{2}

3. If Y = 3cos(log x) + 4sin(log x) show that x^{2 }(d^{2}y ) + (dy ) + y = 0

dx^{2} dx

tan

^{-1}( 5x / 1 - 6x^{2})The answer:( 3 / 1 + 9x

^{2}+ 2 / 1 + 4x^{2})If x = a (θ - sin θ) and y = a (1 - cos θ), find y

_{2}at θ = .find the derivative of cos root x wrt x from first principle??

Find the intervals in which the function f(x) = sin^4x + cos^4x is increasing or decreasing where the range of x is ( 0, pie/2) .

If y = sin (sin x), prove that

d

^{2}y/dx^{2}+ (tan x) dy/dx + y cos^{2}x = 0._{x6 + root 1-y}^{6 = }^{a3(x3-y3). }prove dy/dx = x^{2}/y^{2}*wholeroot 1-y^{6}/1-x^{6}If x

^{p}y^{q}=(x+y)^{p+q}, then prove that dy/dx=y/x.Examine continuity of function f(x) = e

^{1/x}-1 / e^{1/x}+1 at x=0if

xy_{+}_{y}x =_{a}b find dy/dxIf x=tan(1/a logy) Show that (1+x

^{2})d^{2}y/dx^{2}+ (2x-a)dy/dx = 0if x=a sin2t(1+cos2t) and y=b cos2t(1-cos2t) find dy/dx.

if x=2cost -cos2t and y=2sint -sin2t . find d

^{2}y/dx^{2.plzzz help}^{y/x}=x, prove that x^{3}d^{2}y/dx^{2 }= (x.dy/dx - y)^{2}Please solve the following problems.

1. Y = Sin(mSin

^{-1}x) prove that1-x^{2}^{ }- xy^{-1}+m^{2}y = 02

2. Y = Cosec x + Cot x prove that sin x (

d) = y^{2}y^{2}dx

^{2}3. If Y = 3cos(log x) + 4sin(log x) show that x

^{2 }(d) + (^{2}ydy) + y = 0dx

^{2}dx