English

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

Advertisements
Advertisements

Question

Find the second order derivative of the function.

x20

Sum
Advertisements

Solution

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
  Is there an error in this question or solution?
Chapter 5: Continuity and Differentiability - Exercise 5.7 [Page 183]

APPEARS IN

NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 5 Continuity and Differentiability
Exercise 5.7 | Q 183 | Page 183

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

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`


Find the second order derivative of the function.

ex sin 5x


Find the second order derivative of the function.

tan–1 x


Find the second order derivative of the function.

sin (log x)


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


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 = `"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`


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


sec(x + y) = xy


If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1 


If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:


Derivative of cot x° with respect to x is ____________.


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


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.

  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×