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

State whether the following is True or False: If y = e2, then dydx=2e - Mathematics and Statistics

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प्रश्न

State whether the following is True or False:

If y = e2, then `"dy"/"dx" = 2"e"`

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर
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उत्तर

False

shaalaa.com
The Concept of Derivative - Derivatives of Logarithmic Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Differentiation - MISCELLANEOUS EXERCISE - 3 [पृष्ठ १००]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 3 Differentiation
MISCELLANEOUS EXERCISE - 3 | Q III] 7) | पृष्ठ १००

संबंधित प्रश्‍न

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


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


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


If y = elogx then `dy/dx` = ?


Fill in the Blank

If 0 = log(xy) + a, then `"dy"/"dx" =  (-"y")/square`


If y = `e^(ax)`, then `x * dy/dx` = ______.


State whether the following is True or False:

The derivative of `log_ax`, where a is constant is `1/(x.loga)`.


State whether the following is True or False:

If y = log x, then `"dy"/"dx" = 1/"x"`


The derivative of ax is ax log a.


Differentiate log (1 + x2) with respect to ax.


If u = 5x and v = log x, then `("du")/("dv")` is ______


State whether the following statement is True or False:

If y = 4x, then `("d"y)/("d"x)` = 4x  


Find `("d"y)/("d"x)`, if y = (log x)x + (x)logx


Find `("d"y)/("d"x)`, if y = xx + (7x – 1)x 


If xa .yb = `(x + y)^((a + b))`, then show that `("d"y)/("d"x) = y/x`


Find `("d"y)/("d"x)`, if y = x(x) + 20(x) 

Solution: Let y = x(x) + 20(x) 

Let u = `x^square` and v = `square^x`

∴ y = u + v

Diff. w.r.to x, we get

`("d"y)/("d"x) = square/("d"x) + "dv"/square`   .....(i)

Now, u = xx

Taking log on both sides, we get

log u = x × log x

Diff. w.r.to x,

`1/"u"*"du"/("d"x) = x xx 1/square + log x xx square`

∴ `"du"/("d"x)` = u(1 + log x)

∴ `"du"/("d"x) = x^x (1 +  square)`    .....(ii)

Now, v = 20x

Diff.w.r.to x, we get

`"dv"/("d"x") = 20^square*log(20)`     .....(iii)

Substituting equations (ii) and (iii) in equation (i), we get

`("d"y)/("d"x)` = xx(1 + log x) + 20x.log(20)


`int 1/(4x^2 - 1) dx` = ______.


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


Find `dy/dx  "if",y=x^(e^x) `


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Find `dy/dx,"if"  y=x^x+(logx)^x`


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


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


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