Advertisements
Advertisements
Question
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
Advertisements
Solution
`y = a (cost+logtan(t/2)) and x=asint`
`therefore dy/dt=a[d/dt(cost)+d/dt(log tan (t/2))]=a[-sint+cot(t/2)xxsec^2(t/2)xxt/2]=a[-sint+1/(2sin(t/2)cos(t/2))]`
`dy/dt=a(-sint+1/sint)=a((-sin^2t+1)/sint)=a cos^2t/sint`
`dx/dt=a d/dt(sint)=acost`
`therefore dy/dx=(dy/dt)/(dx/dt)=(a (cos^2t/sint))/acost=cost/sint=cott`
`(d^2y)/(dx^2)=d(cott)/dx=-cosec^2tdt/dx=-cosec^2txx1/(acost)=1/(asin^2tcost)`
APPEARS IN
RELATED QUESTIONS
Find the second order derivative of the function.
x2 + 3x + 2
Find the second order derivative of the function.
log x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
log (log x)
If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.
If y = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2)` = 49y.
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
Find `("d"^2"y")/"dx"^2`, if y = `sqrt"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0
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 = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:
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)`.
`"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))`
