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.
ex sin 5x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
log (log x)
If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.
If y = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
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 = `sqrt"x"`
Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
Find `("d"^2"y")/"dx"^2`, if y = log (x).
If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`
If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0
`sin xy + x/y` = x2 – y
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 ____________.
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 = 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))`
