हिंदी

Find the second order derivative of the function. x^20 - Mathematics

Advertisements
Advertisements

प्रश्न

Find the second order derivative of the function.

x20

योग
Advertisements

उत्तर

Let, y = x20

Differentiating both sides with respect to x,

`dy/dx = d/dx x^20`

= `20x^(20 - 1)`

= 20 x19

Differentiating both sides again with respect to x,

`(d^2 y)/dx^2 = 20 d/dx x^19`

= `20 xx 19x^(19 - 1)`

= 380 x18

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.7 [पृष्ठ १८३]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.7 | Q 183 | पृष्ठ १८३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`


If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=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.

x3 log x


Find the second order derivative of the function.

ex sin 5x


If y = 5 cos x – 3 sin x, prove that `(d^2y)/(dx^2) + y = 0`.


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


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 = `"x"^-7`


Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.


Find `("d"^2"y")/"dx"^2`, if y = log (x).


Find `("d"^2"y")/"dx"^2`, if y = 2at, x = at2


Find `("d"^2"y")/"dx"^2`, if y = `"x"^2 * "e"^"x"`


If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0


`sin xy + x/y` = x2 – y


sec(x + y) = xy


(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.


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 = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.


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))`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×