English

State whether the following is True or False: The derivative of xm⋅yn=(x + y)m + n is xy - Mathematics and Statistics

Advertisements
Advertisements

Question

State whether the following is True or False:

The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`

Options

  • True

  • False

MCQ
True or False
Advertisements

Solution

False

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Differentiation - MISCELLANEOUS EXERCISE - 3 [Page 100]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 3 Differentiation
MISCELLANEOUS EXERCISE - 3 | Q III] 9) | Page 100

RELATED QUESTIONS

Find `bb(dy/dx)` in the following:

ax + by2 = cos y


Find `bb(dy/dx)` in the following:

sin2 y + cos xy = k


Find `"dy"/"dx"` ; if y = cos-1 `("2x" sqrt (1 - "x"^2))`


Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`


If ex + ey = e(x + y), then show that `dy/dx = -e^(y - x)`.


Find `"dy"/"dx"` if x = a cot θ, y = b cosec θ


Find `"dy"/"dx"`, if : x = sinθ, y = tanθ


Find `"dy"/"dx"` if : x = cosec2θ, y = cot3θ at θ= `pi/(6)`


Differentiate xx w.r.t. xsix.


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


If x = at2 and y = 2at, then show that `xy(d^2y)/(dx^2) + a` = 0.


If y = x + tan x, show that `cos^2x.(d^2y)/(dx^2) - 2y + 2x` = 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.


Find the nth derivative of the following:

y = e8x . cos (6x + 7)


Choose the correct option from the given alternatives :

If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........


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


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 x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______


`(dy)/(dx)` of `2x + 3y = sin x` is:-


y = `e^(x3)`


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


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


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 = e^(3t), 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`


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×