Advertisements
Advertisements
प्रश्न
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Advertisements
उत्तर
If x = a cos t, y = b sin t
`dx/(dt)` = – a sin t
`dy/(dt)` = b cos t
`dy/dx = (dy/(dt))/(dx/(dt))`
= `(b cos t)/(-a sin t)`
= `(-b)/a cot t`
`(d^2y)/(dx^2) = b/a "cosec"^2t xx (dt)/dx`
= `b/a "cosec"^2t xx (-1)/(a sin t)`
= `-b/a^2 "cosec"^3t`.
APPEARS IN
संबंधित प्रश्न
If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`
Find the second order derivative of the function.
x . cos x
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.
tan–1 x
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 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"`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`
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 = 2at, x = at2
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.
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`.
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)`
