Advertisements
Advertisements
प्रश्न
Find the second order derivative of the function.
sin (log x)
Advertisements
उत्तर
Let, y = sin (log x)
Differentiating both sides with respect to x,
`dy/dx = d/dx sin (log x)`
= `cos (log x) d/dx log x`
= `cos (log x) * 1/x`
= `(cos (log x))/x`
Differentiating both sides again with respect to x,
`d/dx [dy/dx] = d/dx [(cos (log x))/x]`
`(d^2y)/dx^2 = (x d/dx cos (log x) - cos (log x) d/dx (x))/x^2`
= `(x [-sin (log x)] * 1/x - cos (log x * 1))/x^2`
= `(-[sin (log x) + cos (log x)])/x^2`
APPEARS IN
संबंधित प्रश्न
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.
x . cos x
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
tan–1 x
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 ey (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 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 = `"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))`.
Find `("d"^2"y")/"dx"^2`, if y = `"x"^2 * "e"^"x"`
`sin xy + x/y` = x2 – y
tan–1(x2 + y2) = a
(x2 + y2)2 = xy
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 y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
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`.
`"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))`
