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.
x . cos x
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 = cos–1 x, find `(d^2y)/dx^2` in terms of y alone.
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`
Find `("d"^2"y")/"dx"^2`, if y = `sqrt"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 = `"x"^2 * "e"^"x"`
tan–1(x2 + y2) = a
(x2 + y2)2 = xy
If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1
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:
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is ______.
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 ______.
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 = 3 cos(log x) + 4 sin(log x), show that `x^2 (d^2y)/(dx^2) + x dy/dx + y = 0`
