Advertisements
Advertisements
प्रश्न
If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
Advertisements
उत्तर
y = x + tan x
∴ `"dy"/"dx" = "d"/"dx"(x + tanx)`
= 1 + sec2x
and
`(d^2y)/(dx^2) = "d"/"dx"(1 + sec x)^2`
= `"d"/"dx"(1) + "d"/"dx"(sec x)^2`
= 2sec x . sec x tan x
= 2 sec2x tan x
∴ `cos^2x.(d^2y)/(dx^2) - 2y + 2x`
= `cos^2x(2sec^2xtanx) - 2(x + tanx) + 2x`
= `cos^2x xx (2)/(cos^2x) xx tan x - 2x - 2tanx + 2x`
= 2 tan x – 2 tan x
∴ `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 0.
APPEARS IN
संबंधित प्रश्न
Find `bb(dy/dx)` in the following:
2x + 3y = sin y
Find `bb(dy/dx)` in the following:
xy + y2 = tan x + y
Find `bb(dy/dx)` in the following:
x3 + x2y + xy2 + y3 = 81
Show that the derivative of the function f given by
If for the function
\[\Phi \left( x \right) = \lambda x^2 + 7x - 4, \Phi'\left( 5 \right) = 97, \text { find } \lambda .\]
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
If f (x) = |x − 2| write whether f' (2) exists or not.
Write the derivative of f (x) = |x|3 at x = 0.
Find `(dy)/(dx) , "If" x^3 + y^2 + xy = 10`
If x = tan-1t and y = t3 , find `(dy)/(dx)`.
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`
Find `"dy"/"dx"` if : x = a cos3θ, y = a sin3θ at θ = `pi/(3)`
Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`
Differentiate `tan^-1((cosx)/(1 + sinx)) w.r.t. sec^-1 x.`
Differentiate xx w.r.t. xsix.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/(x)) w.r.t tan^-1((2xsqrt(1 - x^2))/(1 - 2x^2))`.
If y = `e^(mtan^-1x)`, show that `(1 + x^2)(d^2y)/(dx^2) + (2x - m)"dy"/"dx"` = 0.
If y = eax.sin(bx), show that y2 – 2ay1 + (a2 + b2)y = 0.
If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.
If y = sin (m cos–1x), then show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" + m^2y` = 0.
If x2 + 6xy + y2 = 10, show that `(d^2y)/(dx^2) = (80)/(3x + y)^3`.
Find the nth derivative of the following : (ax + b)m
Find the nth derivative of the following : eax+b
Find the nth derivative of the following : cos x
Find the nth derivative of the following:
y = e8x . cos (6x + 7)
DIfferentiate `tan^-1((sqrt(1 + x^2) - 1)/x) w.r.t. tan^-1(sqrt((2xsqrt(1 - x^2))/(1 - 2x^2)))`.
Differentiate log `[(sqrt(1 + x^2) + x)/(sqrt(1 + x^2 - x)]]` w.r.t. cos (log x).
If y2 = a2cos2x + b2sin2x, show that `y + (d^2y)/(dx^2) = (a^2b^2)/y^3`
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
Find `"dy"/"dx"` if, xy = log (xy)
If x5· y7 = (x + y)12 then show that, `dy/dx = y/x`
Solve the following:
If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.
Choose the correct alternative.
If `"x"^4."y"^5 = ("x + y")^("m + 1")` then `"dy"/"dx" = "y"/"x"` then m = ?
Find `"dy"/"dx"` if x = `"e"^"3t", "y" = "e"^(sqrt"t")`.
If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______
`(dy)/(dx)` of `2x + 3y = sin x` is:-
If y = `e^(m tan^-1x)` then show that `(1 + x^2) (d^2y)/(dx^2) + (2x - m) (dy)/(dx)` = 0
If `tan ((x + y)/(x - y))` = k, then `dy/dx` is equal to ______.
Find `dy/dx if, x= e^(3t), y = e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if , x = `e^(3t), y = e^(sqrtt)`
Find `dy / dx` if, x = `e^(3t), y = e^sqrt t`
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
