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

If x = atta(t-1t), y = atta(t+1t), where t be the parameter, then dddydx = ? - Mathematics and Statistics

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प्रश्न

If x = `"a"("t" - 1/"t")`, y = `"a"("t" + 1/"t")`, where t be the parameter, then `("d"y)/("d"x)` = ?

पर्याय

  • `x/y`

  • `(-x)/y`

  • `y/x`

  • `(-y)/x`

MCQ
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उत्तर

`bb(x/y)`

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Derivatives of Parametric Functions
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.3: Differentiation - Q.1

संबंधित प्रश्‍न

Find `"dy"/"dx"`, if x = `("u" + 1/"u")^2, "y" = (2)^(("u" + 1/"u"))`


Find `"dy"/"dx"`, if x = `sqrt(1 + "u"^2), "y" = log (1 + "u"^2)`


Solve the following.

If x = `"a"(1 - 1/"t"), "y" = "a"(1 + 1/"t")`, then show that `"dy"/"dx" = - 1`


If x = `(4t)/(1 + t^2),  y = 3((1 - t^2)/(1 + t^2))` then show that `dy/dx = (-9x)/(4y)`.


If x = t . log t, y = tt, then show that `dy/dx - y = 0`.


If x = 2at2 , y = 4at, then `dy/dx = ?`


If x sin(a + y) + sin a cos(a + y) = 0 then show that `("d"y)/("d"x) = (sin^2("a" + y))/(sin"a")`


Choose the correct alternative:

If x = 2am, y = 2am2, where m be the parameter, then `("d"y)/("d"x)` = ? 


State whether the following statement is True or False:

If x = 2at, y = 2a, where t is parameter, then `("d"y)/("d"x) = 1/"t"`


Find `("d"y)/("d"x)`, if x = em, y = `"e"^(sqrt("m"))`

Solution: Given, x = em and y = `"e"^(sqrt("m"))`

Now, y = `"e"^(sqrt("m"))`

Diff.w.r.to m,

`("d"y)/"dm" = "e"^(sqrt("m"))("d"square)/"dm"`

∴ `("d"y)/"dm" = "e"^(sqrt("m"))*1/(2sqrt("m"))`    .....(i)

Now, x = em

Diff.w.r.to m,

`("d"x)/"dm" = square`    .....(ii)

Now, `("d"y)/("d"x) = (("d"y)/("d"m))/square`

∴ `("d"y)/("d"x) = (("e"sqrt("m"))/square)/("e"^"m")`

∴  `("d"y)/("d"x) = ("e"^(sqrt("m")))/(2sqrt("m")*"e"^("m")`


If x = `sqrt(1 + u^2)`, y = `log(1 + u^2)`, then find `(dy)/(dx).`


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


Find `dy/dx` if, x = e3t, y = `e^((4t + 5))`


If x = f(t) and y = g(t) are differentiable functions of t, then prove that:

`dy/dx = ((dy//dt))/((dx//dt))`, if `dx/dt ≠ 0`

Hence, find `dy/dx` if x = a cot θ, y = b cosec θ.


Suppose y = f(x) is differentiable function of x and y is one-one onto, `dy/dx ≠ 0`. Also, if x = f–1(y) is differentiable, then prove that `dx/dy = 1/((dy/dx))`, where `dy/dx ≠ 0`

Hence, find `d/dx(tan^-1x)`.


Find `dy/dx` if, x = `e^(3t)`, y = `e^(4t+5)`


Find `dy/dx if, x = e^(3t),y=e^((4t+5))`


 Find `dy/dx` if,

`x = e ^(3^t), y = e^((4t + 5))`


Find `dy/dx` if x= `e^(3t)`, y =`e^((4t+5))`


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