हिंदी

State whether the following is True or False: If y = ex, then dydx = ex - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False:

If y = ex, then `("d"y)/("d"x)` = ex 

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

True

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.3: Differentiation - Q.3

संबंधित प्रश्न

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


Find `dy/dx` if, y = `sqrt(x + 1/x)`


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


Find `"dy"/"dx"` if, y = log(10x4 + 5x3 - 3x2 + 2)


Fill in the Blank.

If 3x2y + 3xy2 = 0, then `(dy)/(dx)` = ______.


`d/dx(10^x) = x*10^(x - 1)`


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(5x + 7)/(2x - 13)`


If y = sec (tan−1x), then `dy/dx` at x = 1 is ______.


If y = `("e")^((2x + 5))`, then `("d"y)/("d"x)` is ______


y = (6x4 – 5x3 + 2x + 3)6, find `("d"y)/("d"x)`

Solution: Given,

y = (6x4 – 5x3 + 2x + 3)6 

Let u = `[6x^4 - 5x^3 + square + 3]`

∴ y = `"u"^square`

∴ `("d"y)/"du"` = 6u6–1

∴ `("d"y)/"du"` = 6(  )5 

and `"du"/("d"x) = 24x^3 - 15(square) + 2`

By chain rule,

`("d"y)/("d"x) = ("d"y)/square xx square/("d"x)`

∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^square xx (24x^3 - 15x^2 + square)`


If y = (sin x2)2,  then `("d"y)/("d"x)` is equal to ______.


If y = `(cos x)^((cosx)^((cosx))`, then `("d")/("d"x)` = ______.


If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`


If f(x) = |cos x|, find f'`((3pi)/4)`


y = sin (ax+ b)


y = `2sqrt(cotx^2)`


If ax2 + 2hxy + by2 = 0, then prove that `(d^2y)/(dx^2)` = 0.


If `y = root5(3x^2 + 8x + 5)^4`, find `dy/dx`


Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`


The differential equation of (x - a)2 + y2 = a2 is ______ 


If y = `tan^-1((6x - 7)/(6 + 7x))`, then `dy/dx` = ______.


Solve the following:

If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`


Find `dy/dx` if, y = `e^(5x^2-2x+4)`


Find `dy/dx` if, `y=e^(5x^2-2x+4)`


Find `(dy) / (dx)` if, `y = e ^ (5x^2 - 2x + 4)`


If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`


Find `dy/dx` if, `y = e^(5x^2 - 2x +  4)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×