Advertisements
Advertisements
प्रश्न
Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2
उत्तर
x = at2
Differentiating both sides w.r.t. t, we get
`"dx"/"dt" = "a" "d"/"dx" ("t"^2) = "a"("2t")`
∴ `"dx"/"dt" = "2at"` ....(i)
y = 2at
Differentiating both sides w.r.t. t, we get
`"dy"/"dt" = "2a" "d"/"dt" ("t")`
∴ `"dy"/"dt"` = 2a
∴ `"dy"/"dx" = ("dy"/"dt")/("dx"/"dt") = "2a"/"2at" = 1/"t"`
Again, differentiating both sides w.r.t. x, we get
`("d"^2"y")/"dx"^2 = (-1)/"t"^2 * "dt"/"dx" = (-1)/"t"^2 xx 1/"2at"` ....[From (i)]
`= (- 1)/"2at"^3`
APPEARS IN
संबंधित प्रश्न
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`
Find the second order derivative of the function.
x2 + 3x + 2
Find the second order derivative of the function.
`x^20`
Find the second order derivative of the function.
x3 log x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
tan–1 x
If y = 3 cos (log x) + 4 sin (log x), show that x2 y2 + xy1 + y = 0
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2) = 49y`
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) =((dy)/(dx))^2`
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
If x7 . y9 = (x + y)16 then show that `"dy"/"dx" = "y"/"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^-7`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
Find `("d"^2"y")/"dx"^2`, if y = `"x"^2 * "e"^"x"`
If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`
tan–1(x2 + y2) = a
If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1
If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
Derivative of cot x° with respect to x is ____________.
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Read the following passage and answer the questions given below:
|
The relation between the height of the plant ('y' in cm) with respect to its exposure to the sunlight is governed by the following equation y = `4x - 1/2 x^2`, where 'x' is the number of days exposed to the sunlight, for x ≤ 3.
|
- Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
- Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?
`"Find" (d^2y)/(dx^2) "if" y=e^((2x+1))`
Find `(d^2y)/dx^2 if, y = e^((2x + 1))`
Find `(d^2y)/dx^2 "if," y= e^((2x+1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/dx^2, "if" y = e^((2x+1))`
Find `(d^2y)/dx^2` if, `y = e^((2x+1))`
