मराठी

Find the second order derivative of the function. x2 + 3x + 2

Advertisements
Advertisements

प्रश्न

Find the second order derivative of the function.

x2 + 3x + 2

बेरीज
Advertisements

उत्तर

Let, y = x2 + 3x + 2

Differentiating both sides with respect to x,

`dy/dx` = 2x + 3

Differentiating both sides again with respect to x,

`d/dx (dy/dx) = (d^2 y)/dx^2`

= `d/dx` (2x + 3)

= 2

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity and Differentiability - Exercise 5.7 [पृष्ठ १८३]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
पाठ 5 Continuity and Differentiability
Exercise 5.7 | Q 1 | पृष्ठ १८३

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

If x = a sin t and `y = a (cost+logtan(t/2))` ,find `((d^2y)/(dx^2))`


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.

x3 log x


If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2)` = 49y.


If ey (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^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"^"log x"`


If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`


(x2 + y2)2 = xy


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.


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 ______.


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.

  1. Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
  2. 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))`


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 \[f(x)\]?


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 \[\frac{d^2y}{dx^2}\]?


Which equation is satisfied by \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\]?


If \[y=\sin^{-1}x\], what is \[\frac{dy}{dx}\]?


What equation is obtained after multiplying through by \[\sqrt{1-x^2}\] in the derivation for \[y=\sin^{-1}x\]?


For \[y=\sin^{-1}x\], which relation uses \[y_{1}\] for the first derivative?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×