हिंदी

Find d2ydy2, if y = e4x - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find `(d^2y)/(dy^2)`, if y = e4x

विकल्प

  • 8 e4x

  • 16 e4x

  • 13 e4x

  • 22 e4x

MCQ

उत्तर

16 e4x

Explanation:

y = e4x

`dy/dx = e^(4x). d/dx(4x)` = e4x.4 = 4.e4x

`(d^2y)/(dy^2) = d/(dy)(4.e^(4x))` = 4.e4x.4 = 16. e4x

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2024-2025 (March) Model set 1 by shaalaa.com

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Find `dy/dx` in the following:

xy + y2 = tan x + y


Find `dy/dx` in the following.

x3 + x2y + xy2 + y3 = 81


Find the derivative of the function f defined by f (x) = mx + c at x = 0.


Write the derivative of f (x) = |x|3 at x = 0.


Find `(dy)/(dx) , "If"   x^3 + y^2 + xy = 10`


Find `"dy"/"dx"`, if : x = `(t + 1/t)^a, y = a^(t+1/t)`, where a > 0, a ≠ 1, t ≠ 0.


Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`


Differentiate `sin^-1((2x)/(1 + x^2))w.r.t. cos^-1((1 - x^2)/(1 + x^2))`


Differentiate `tan^-1((x)/(sqrt(1 - x^2))) w.r.t. sec^-1((1)/(2x^2 - 1))`.


Find `(d^2y)/(dx^2)` of the following : x = a cos θ, y = b sin θ at θ = `π/4`.


If y = `e^(mtan^-1x)`, show that `(1 + x^2)(d^2y)/(dx^2) + (2x - m)"dy"/"dx"` = 0.


If `sec^-1((7x^3 - 5y^3)/(7^3 + 5y^3)) = "m", "show"  (d^2y)/(dx^2)` = 0.


If 2y = `sqrt(x + 1) + sqrt(x - 1)`, show that 4(x2 – 1)y2 + 4xy1 – y = 0.


Find the nth derivative of the following : cos x


Find the nth derivative of the following:

y = e8x . cos (6x + 7)


Choose the correct option from the given alternatives :

If y = sec (tan –1x), then `"dy"/"dx"` at x = 1, is equal to


Choose the correct option from the given alternatives :

If y = sin (2sin–1 x), then dx = ........


Choose the correct option from the given alternatives :

If y = `tan^-1(x/(1 + sqrt(1 - x^2))) + sin[2tan^-1(sqrt((1 - x)/(1 + x)))] "then" "dy"/"dx"` = ...........


Choose the correct option from the given alternatives :

If y = `a cos (logx) and "A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, then the values of A, B, C are


Differentiate the following w.r.t. x : `tan^-1((sqrt(x)(3 - x))/(1 - 3x))`


If `sqrt(y + x) + sqrt(y - x)` = c, show that `"dy"/"dx" = y/x - sqrt(y^2/x^2 - 1)`.


If `xsqrt(1 - y^2) + ysqrt(1 - x^2)` = 1, then show that `"dy"/"dx" = -sqrt((1 - y^2)/(1 - x^2)`.


If x sin (a + y) + sin a . cos (a + y) = 0, then show that `"dy"/"dx" = (sin^2(a + y))/(sina)`.


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`


If y = Aemx + Benx, show that y2 – (m + n)y1 + mny = 0.


Find `"dy"/"dx" if, sqrt"x" + sqrt"y" = sqrt"a"`


Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81


Find `"dy"/"dx"` if, xy = log (xy)


Solve the following:

If `"x"^5 * "y"^7 = ("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 y = 5x . x5, then `"dy"/"dx" = ?` 


Choose the correct alternative.

If ax2 + 2hxy + by2 = 0 then `"dy"/"dx" = ?` 


If y = `("x" + sqrt("x"^2 - 1))^"m"`, then `("x"^2 - 1) "dy"/"dx"` = ______.


If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`


Find `"dy"/"dx"` if x = `"e"^"3t",  "y" = "e"^(sqrt"t")`.


If x = a t4 y = 2a t2 then `("d"y)/("d"x)` = ______


If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.


Differentiate w.r.t x (over no. 24 and 25) `e^x/sin x`


y = `e^(x3)`


If y = `e^(m tan^-1x)` then show that `(1 + x^2) (d^2y)/(dx^2) + (2x - m) (dy)/(dx)` = 0


If 2x + 2y = 2x+y, then `(dy)/(dx)` is equal to ______.


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`


If log (x + y) = log (xy) + a then show that, `dy/dx = (−y^2)/x^ 2`


If log (x+y) = log (xy) + a then show that, `dy/dx= (-y^2)/(x^2)`


If y = `(x + sqrt(x^2 - 1))^m`, show that `(x^2 - 1)(d^2y)/(dx^2) + xdy/dx` = m2y


Find `dy / dx` if, x = `e^(3t), y = e^sqrt t` 


Find `dy/dx` if, x = e3t, y = `e^sqrtt`


If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×