If y=sin(sinx) then prove that (d^2y)/...

If `y=sin(sinx)` then prove that
`(d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2x=0`

Continuity and Differentiability
NAGEEN PRAKASHAN|Exercise Exercies 5m|19 Videos
Continuity and Differentiability
NAGEEN PRAKASHAN|Exercise Exercies 5n|11 Videos
Continuity and Differentiability
NAGEEN PRAKASHAN|Exercise Exercies 5k|12 Videos
APPLICATIONS OF INTEGRALS
NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos
DETERMINANTS
NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

If y=sin(sin x), prove that (d^(2)y)/(dx^(2))+tan x(dy)/(dx)+y cos^(2)x=0

If y=sin(sin x), prove that (d^(2)y)/(dx^(2))+tan x(dy)/(dx)cos^(2)x=0

If y=5sinx-3sinx , prove that : (d^(2)y)/(dx^(2))+y=0 .

If y=sin(log x), then prove that (x^(2)d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0

If y=sin^(-1)x ,then prove that (1-x^(2))(d^(2)y)/(dx^(2))=x(dy/dx)

If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2=0 .

If y=sin^(-1)x then prove that (1-x^(2))(d^(y))/(dx^(2))-x(dy)/(dx)=0

If y=sin(log x), prove that x^(2)(d^(2)y)/(dx^(2))+x(dy)/(dx)+y=0

If y=A cos x+B sin x then prove that (d^(2)y)/(dx^(2))+y=0

Find the 2nd derivative if x^3 log x with respect to x.
Text Solution
|
If y=tan^(-1)x^3 then find (d^2y)/(dx^(2)).
Text Solution
|
Find the 2nd dervative of e^(ax+b) with respect to x.
Text Solution
|
If y=x+cotx then prove that sin^2x(d^2y)/(dx^2)-2y2x=0.
Text Solution
|
If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .
Text Solution
|
If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0
Text Solution
|
(i) If y=asin(log x) then prove that x^(2)*(d^2y)/(dx^2)+x(dy)/(dx)+y=...
Text Solution
|
If y=(sin^(-1)x)^2 then prove that (1-x^(2))(d^2y)/(dx^2)-x(dy)/(dx)-2...
Text Solution
|
If y=sin(sinx) then prove that (d^2y)/(dx^2)+tanx. (dy)/(dx)+y cos^2...
Text Solution
|
IF y=e^(tan^(-1)x) then prove that : (1-x^(2))(d^2y)/(dx^2)+(2x-1)(d...
Text Solution
|
If y^3-3ax^2+x^3=0, then prove that (d^2y)/(dx^2)+(2a^2x^2)/(y^5) = 0
Text Solution
|
If y=(t a n^(-1)\ x^2) , show that (x^2+1)^2(d^2\ y)/(dx^2)+2x(x^2+1)(...
Text Solution
|
If y=e^tanx then prove that: cos^2x(d^2y)/(dx^2)-(1+sin2x)(dy)/dx=0
Text Solution
|
If y=A e^(-k t)cos(p t+c), then prove that (d^2y)/(dt^2)+2k(dy)/(dx)+n...
Text Solution
|
If x=at^2,y=2 at then find (d^2y)/(dx^2).
Text Solution
|
If x=a(t-sint), y=a(1-cost) then find (d^2y)/(dx^2).
Text Solution
|
If x=sint" and "y=sin mt" then prove that "sqrt(1-x^2)(d^2y)/(dx^2)-xd...
Text Solution
|
If y=(sin^(-1)x)^2+(cos^(-1)x)^2, then prove that (1-x^2)y2-xy(1)-4=0.
Text Solution
|