मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Find dydx if, y = log(log x) - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

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

बेरीज
Advertisements

उत्तर

y = log(log x)

Differentiating both sides w.r.t.x, we get

`"dy"/"dx" = "d"/"dx"` [log (log x)]

`= 1/(log "x") * "d"/"dx" (log "x")`

`= 1/(log "x") * 1/"x"`

∴ `"dy"/"dx" = 1/("x" * log "x")`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Differentiation - EXERCISE 3.1 [पृष्ठ ९१]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Differentiation
EXERCISE 3.1 | Q 2. 1) | पृष्ठ ९१

संबंधित प्रश्‍न

if `y = tan^2(log x^3)`, find `(dy)/(dx)`


Solve : `"dy"/"dx" = 1 - "xy" + "y" - "x"`


Find `"dy"/"dx"` if ex+y = cos(x – y)


Find the second order derivatives of the following : `2x^5 - 4x^3 - (2)/x^2 - 9`


Find the second order derivatives of the following : e4x. cos 5x


Find the second order derivatives of the following : xx 


Find `"dy"/"dx"` if, y = log(ax2 + bx + c) 


Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`


Find `"dy"/"dx"` if, y = `5^(("x" + log"x"))`


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 25 + 30x  – x2.


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


Find `"dy"/"dx"`, if y = `2^("x"^"x")`.


State whether the following statement is True or False:

If y = ex, then `("d"^2y)/("d"x^2)` = ex 


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)`


Derivative of ex sin x w.r.t. e-x cos x is ______.


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


Differentiate `sqrt(tansqrt(x))` w.r.t. x


If f(x) = |cos x – sinx|, find `"f'"(pi/6)`


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


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


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


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


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


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


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


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


Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = 12 + 10`x + 25x^2`


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×