Advertisements
Advertisements
Question
Find the second order derivative of the function.
log x
Advertisements
Solution
Let, y = log x
Differentiating both sides with respect to x,
`dy/dx = d/dx log x`
`dy/dx = 1/x`
Differentiating both sides again with respect to x,
`(d^2y)/(dx^2 ) = d/dx [1/x]`
= `d/dx [x^-1]`
= `-1 x^(-1-1)`
= −1 x−2
= `-1/x^2`
APPEARS IN
RELATED QUESTIONS
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.
x3 log x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
log (log x)
If y = cos–1 x, find `(d^2y)/dx^2` in terms of y alone.
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
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"^-7`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"x"`
Find `("d"^2"y")/"dx"^2`, if y = log (x).
If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0
tan–1(x2 + y2) = a
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 x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Read the following passage and answer the questions given below:
|
The relation between the height of the plant ('y' in cm) with respect to its exposure to the sunlight is governed by the following equation y = `4x - 1/2 x^2`, where 'x' is the number of days exposed to the sunlight, for x ≤ 3.
|
- Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
- Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?
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))`
Let \[y=f(x)\]. What is the first derivative of \[y\] with respect to \[x\]?
Which of the following is NOT a stated notation for the second derivative of \[f(x)\]?
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 \[\frac{d^2y}{dx^2}\]?
Which equation is satisfied by \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\]?
After differentiating \[\sqrt{1-x^2}\cdot\frac{dy}{dx}=1\], which equation results?
What equation is obtained after multiplying through by \[\sqrt{1-x^2}\] in the derivation for \[y=\sin^{-1}x\]?
Which equation follows from \[(1-x^2)\cdot2y_{1}y_{2}+y_{1}^{2}(0-2x)=0\]?
