Advertisements
Advertisements
Question
Find the second order derivative of the function.
x3 log x
Advertisements
Solution
Let, y = x3 log x
Differentiating both sides with respect to x,
`dy/dx = x^3 d/dx log x + log x d/dx x^3`
= `x^3 * 1/x + log x * 3x^2`
= x2 + 3x2 log x
Differentiating both sides again with respect to x,
`(d^2 y)/dx^2 = d/dx x^2 + 3 [x^2 d/dx log x + log x d/dx x^2]`
= `2x + 3 [x^2 * 1/x + log x * 2x]`
= 2x + 3x + 6x log x
= 5x + 6x log x
= x (5 + 6 log x)
APPEARS IN
RELATED QUESTIONS
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.
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 = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
If y = Aemx + Benx, show that `(d^2y)/dx^2 - (m+ n) (dy)/dx + mny = 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 = `"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 = log (x).
If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`
`sin xy + x/y` = x2 – y
(x2 + y2)2 = xy
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 ______.
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))`
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))`
