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 y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`
If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`
Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`
Find the second order derivative of the function.
x2 + 3x + 2
Find the second order derivative of the function.
x . cos x
Find the second order derivative of the function.
ex sin 5x
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.
If x7 . y9 = (x + y)16 then show that `"dy"/"dx" = "y"/"x"`
If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`
Find `("d"^2"y")/"dx"^2`, if y = log (x).
Find `("d"^2"y")/"dx"^2`, if y = `"x"^2 * "e"^"x"`
sec(x + y) = xy
(x2 + y2)2 = xy
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"`
Derivative of cot x° with respect to x 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 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))`
If y = 3 cos(log x) + 4 sin(log x), show that `x^2 (d^2y)/(dx^2) + x dy/dx + y = 0`
Find `(d^2y)/dx^2` if, `y = e^((2x+1))`
