If y= sin^-1x/(1-x^{2)1/2 show that (1-x2)d2y/dx2 - 3x dy /dx -y =0}

If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin² (a + y) ] / sin a.

Differentiate

if y= xsin^-1x /(1-x² )^1/2

If X=2cost-cos2t and Y=2sint-sin2t, then prove that

dy/dx=tan(3t/2)

If y³ + x³ -3axy = 0, PT d²y/dx² = -2a³xy/(y²-ax)³

If y=e^acos-1x ; -12)d²y/dx² - x dy/dx - a²y =0

find dy/dx

tan(x+y)+tan(x-y)=1

If tan^-1 [ (x² - y²)/ (x² + y²) ] = a ; prove that dy/dx = x( 1 - tanA) / y ( 1 + tanA)

Show that the function f defined as follows, is continuous at x=2. but not differentiable there at: f(x)={3x-2, 0<x<=1

2x^​2-x, 1<x<=2

5x-4, x>2}

if x=a{(1+t²⁾/(1-t²)} and y=2t/(1-t²) find dy/dx.

differentiate y= (x)^_cosx + (cosx)^sinx

Differentiate w.r.t x:

log(cosecx-cotx)

f(x) = max. (sin x , cos x ) for all x belongs to R . Then number of critical points belongs to ( -2pi , 2pi ) is/ are

(a) 5 (b) 4

(c) 7 (d) none of these

if y(x²+1)^1/2= log ((x²+1) - x)

show that

(x²+1) dy/dx + xy + 1 =0

If f(x) = log_x (log_ex), then f`(x) at x=e is equal to???

What is RHD and LHD explain with a n example.

Show that f(x)=

{ (e^1/x -1)/(e^1/x +1) , x not equal to 0 is discontinuous at x=0.

0 , x=0

If y=(cosx)^lnx +(lnx)^x

find dy/dx

Differentiate sin-¹x w.r.t log( 1+x )

how does a kink in the graph of the function represents the point of non-differentiability? explain in details with examples

f(x) = x³ + bx² +ax on [1,3] .Rolles theorem holds for c= 2 + 1/3^1/2 .Find a and b

show that every constant function is continuous?

If x sin ( A + y) + sinA cos (A + y) = 0, prove that dy/dx = [ sin²(a + y)] / [ sin (a + y) - ycos ( a + y ) ]

Are the proofs of theorems important from the exam point of view? I mean, will we be asked to prove theorems given in the maths textbook in the boards?

If siny + e ^{- x cos y} = e then dy/dx at (1,╥)is......??

Sir i do not agree to you completely...

It is said that log of x to base x is equal to 1 then why is it not log of 1 to base 1 is equal to 1?????

and i did not understand the reasoning behind your saying 0/0 for it...

If y^1/n + y^-1/n = 2x, the (1-x^2)y2 + xy1 =

1) -n^2y 2) n^2y 3) 0 4) none of these

Pls give detailed solution and its explaination :

1) If f(x) = 1/3 { f( x+1) + 5/ f( x+2) } and f(x) 0 for all x belongs to R then lim x-- oo f(x) = ???

a) 0 b) (2/5)^1/2 c) ( 5/2 )^1/2 d) infintiy

2) If k = lim x --- oo ( E1000k =1 ( x+k)m / xm + 101000 ) and ( m 101) then k = ???

a) 10 b) 102 c) 103 d) 104

(* oo implies infinity. E implies summation running from k =1 to 1000)

if y= log tan ( pi/4+ x/2)

show that dy/dx - sec x = 0

If x^myⁿ= (x+y)^m+nprove thatdy/dx=y/x?

x^m sin(1 / x) , x is not equal to 0

Show that the function ƒ(x) = is

0 , x = 0

(i) differentialble at x = 0, if m1

(ii) continous but not differentiable at x = 0, if 0

(iii) neither continous nor differentiable, if m ≤ 0

If f(x) = (log_{cot x} tanx) (log_{tan x} cot x)^-1 + tan^-1 (4x / 4 - x² ), then f`(2) is equal to????

let g(x) be the inverse of an invertible function f(x) which is derivatable at x=3. If f(3)=9 and f'(3)=9, write the calue of g'(9).

dy/dx of y= log(sinx/1+cosx)

wat is log00??????

also log1 to any base is zero, then log 1 to base 1 is what???

If y = logⁿ x, where logⁿ means log log log (repeated n times), then x log x log²x log³x. log^n-1

x logⁿ x dy/dx is equal to???

pl can some one differentiate y=sin(sin(log 3x))