Advertisements
Advertisements
प्रश्न
Find the second order derivative of the function.
log (log x)
Advertisements
उत्तर
Let, y = log (log x)
Differentiating both sides with respect to x,
`dy/dx = d/dx log (log x)`
= `1/(log x). d/dx (log x)`
= `1/(log x) xx 1/x`
= `1/(x log x)`
= (x log x)−1
Differentiating both sides again with respect to x,
`d/dx [dy/dx] = d/dx [(x log x)^-1]`
`(d^2y)/dx^2 = -1 (x log x)^(-1-1) d/dx (x log x)`
= `-1 (x log x)^-2 [x d/dx (log x) + log x d/dx (x)]`
= `-1 xx 1/(x log x)^2 [x xx 1/x + log x (1)]`
= `(-(1 + log x))/ (x log x)^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.
x20
Find the second order derivative of the function.
x . cos x
Find the second order derivative of the function.
ex sin 5x
If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.
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
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 = `"x"^2 * "e"^"x"`
tan–1(x2 + y2) = a
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.
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 y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.
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))`
When is the second order derivative of \[y\] with respect to \[x\] defined?
Which expression defines the second order derivative of \[y\] with respect to \[x\]?
Which of the following is NOT a stated notation for the second derivative of \[f(x)\]?
Higher order derivatives are obtained by which process?
If \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{dy}{dx}\]?
For \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{d^2y}{dx^2}\]?
If \[y=\sin^{-1}x\], what is \[\frac{dy}{dx}\]?
After differentiating \[\sqrt{1-x^2}\cdot\frac{dy}{dx}=1\], which equation results?
For \[y=\sin^{-1}x\], which relation uses \[y_{1}\] for the first derivative?
Differentiating \[(1-x^2)y_{1}^{2}=1\] gives which expression?
Which equation follows from \[(1-x^2)\cdot2y_{1}y_{2}+y_{1}^{2}(0-2x)=0\]?
