Advertisements
Advertisements
प्रश्न
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) =((dy)/(dx))^2`
उत्तर
Given, ey (x + 1) = 1 ...(1)
or, (x + 1) ey = 1
Differentiating both sides with respect to x,
⇒ `1 · ey + (x + 1) ey dy/dx = 0`
`=> e^y + 1 * dy/dx = 0` .... [Putting the value of ey(x + 1) from equation (1)]
`=> dy/dx = - e^y`
Differentiating both sides again with respect to x,
`(d^2 y)/dx^2 = -e^y dy/dx` ...(putting -ey = `dy/dx`)
`= (dy/dx)(dy/dx) = (dy/dx)^2`
Hence, `(d^2 y)/dx^2 = (dy/dx)^2`
APPEARS IN
संबंधित प्रश्न
If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`
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.
x3 log x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
log (log x)
Find the second order derivative of the function.
sin (log 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 = 500e7x + 600e–7x, show that `(d^2y)/(dx^2) = 49y`
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 = `"x"^-7`
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
`sin xy + x/y` = x2 – y
tan–1(x2 + y2) = a
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 ______.
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 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)`
If y = 3 cos(log x) + 4 sin(log x), show that `x^2 (d^2y)/(dx^2) + x dy/dx + y = 0`
