Advertisements
Advertisements
प्रश्न
Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2
Advertisements
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))`
Find the second order derivative of the function.
x20
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
log (log x)
If y = cos–1 x, find `(d^2y)/dx^2` in terms of y alone.
If x7 . y9 = (x + y)16 then show that `"dy"/"dx" = "y"/"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = log (x).
`sin xy + x/y` = x2 – y
sec(x + y) = xy
If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
The derivative of cos–1(2x2 – 1) w.r.t. cos–1x is ______.
If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:
Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, p'i(x) and p''i(x) be the first and second order derivatives of pi(x) respectively. Let,
A(x) = `[(p_1(x), p_1^'(x), p_1^('')(x)),(p_2(x), p_2^'(x), p_2^('')(x)),(p_3(x), p_3^'(x), p_3^('')(x))]`
and B(x) = [A(x)]T A(x). Then determinant of B(x) ______
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
`"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))`
If \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{dy}{dx}\]?
If \[y=\sin^{-1}x\], what is \[\frac{dy}{dx}\]?
For \[y=\sin^{-1}x\], which relation uses \[y_{1}\] for the first derivative?
