If y=e^xcosx , prove that (d^2y)/(dx^2)=...

If `y=e^xcosx` , prove that `(d^2y)/(dx^2)=2\ e^xcos(x+pi/2)` .

FUNCTION
RD SHARMA ENGLISH|Exercise All Questions|406 Videos
INCREASING AND DECREASING FUNCTION
RD SHARMA ENGLISH|Exercise All Questions|232 Videos

Similar Questions

Explore conceptually related problems

If y=e^xcosx , prove that (dy)/(dx)=sqrt(2)\ e^xcos(x+pi/4)

If y=e^-x cos x , show that (d^2y)/(dx^2)= 2e^-x sin x

If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.

If y=e^x+e^-x , prove that (dy)/(dx)=sqrt(y^2-4)

If y=e^x(sin x+cosx) prove that (d^2y)/(dx^2)-2 (dy)/(dx)+2y=0 .

If y=log(sinx) , prove that (d^3y)/(dx^3)=2cosx cos e c^3x .

If y=e^x(sinx+cosx) prove that (d^2y)/(dx^2)-2(dy)/(dx)+2y=0 .

If y=e^x+e^(-x) , prove that (dy)/(dx)=sqrt(y^2-4)

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

If e^x+e^y=e^(x+y) , prove that (dy)/(dx)+e^(y-x)=0

If x=a(cost+tsint) and y=a(sint-tcost), then find the value of (d^2y)...
Text Solution
|
If y=(cot^(-1)x)^2 , prove that y2(x^2+1)^2+2x(x^2+1)y1=2 .
Text Solution
|
If y=e^xcosx , prove that (d^2y)/(dx^2)=2\ e^xcos(x+pi/2) .
Text Solution
|
If x=cos t + (log tant)/2, y=sin t, then find the value of (d^2y)/(dt^...
Text Solution
|
Find A and B so that y=Asin3x+bcos3x satisfies the equation (d^2y)/(d...
Text Solution
|
If x=asint-bcost ,y=acost+bsint ,"p r o v et h a t" (d^2y)/(dx^2)=-...
Text Solution
|
If y=e^(ex) (ax+b), show that y^2-4y1+4y=0
Text Solution
|
If x=asectheta,y=btantheta,"prove that"(d^2y)/(dx^2)=-(b^4)/(a^2y^3)
Text Solution
|
If y=e^"tan"^((-1)"x")), prove that (1+x^2)y2+(2x-1)y1=0.
Text Solution
|
If y=(sin^(-1)x)^2 ,prove that (1-x^2)y2-x y1-2=0.
Text Solution
|
If y={"log"(x+sqrt(x^2+1))}^2,"show that"(1+x^2)(d^2y)/(dx^2)+x(dy)/(...
Text Solution
|
If x=sin(1/alogy),"show that"(1-x^2)y2-xy1-a^2y=0.
Text Solution
|
If y=x+tan x, show that cos^2 x (d^2y)/(dx^2)-2y+2x=0
Text Solution
|
If y=e^-x cos x, show that (d^2y)/(dx^2)= 2e^-x sin x
Text Solution
|
If y=log(sinx),"p r o v et h a t"(d^3)/(dx^3)=2cosxcos e c^3xdot
Text Solution
|
If y=x^3logx ,"prove that"(d^4y)/(dx^4)=6/xdot
Text Solution
|
If y=(logx)/x ,show\ tha t(d^2y)/(dx^2)=(2logx-3)/(x^3)
Text Solution
|
If y=2 sin x+3cos x, show that (d^2y)/(dx^2)+y=0
Text Solution
|
Find . (d^2y)/(dx^2),ifx=a t^2,y=2a t.
Text Solution
|
If x=sin theta,y=cosptheta,p rov e \ t h a t (1-x^2)y2-x y1+p^2y=0,w ...
Text Solution
|