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 = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`
If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`
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.
x2 + 3x + 2
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.
log x
Find the second order derivative of the function.
x3 log x
Find the second order derivative of the function.
ex sin 5x
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 0`.
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 = `"x"^-7`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"x"`
`sin xy + x/y` = x2 – y
sec(x + y) = xy
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 ______.
If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) 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 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))`
Find `(d^2y)/dx^2` if, `y = e^((2x+1))`
