English

Find the derivative of x2 cosx. - Mathematics

Advertisements
Advertisements

Question

Find the derivative of x2 cosx.

Sum

Solution

Let y = x2 cosx

Differentiating both sides with respect to x, we

`(dy)/(dx) = d/(dx)(x^2 cos x)`

= `x^2 d/(dx) (cos x) + cos x d/(dx) (x^2)`

= `x^2(- sinx) + cosx (2x)`

= `2x cosx - x^2 sinx`

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Limits and Derivatives - Solved Examples [Page 232]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 11
Chapter 13 Limits and Derivatives
Solved Examples | Q 13 | Page 232

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(px+ q) (r/s + s)`


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(1 + 1/x)/(1- 1/x)`


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`a/x^4 = b/x^2 + cos x`


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`4sqrtx - 2`


Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(ax + b)n


Find the derivative of f (x) = x2 − 2 at x = 10


Find the derivative of the following function at the indicated point:


x ex


Differentiate of the following from first principle:

(−x)−1


Differentiate each of the following from first principle: 

sin x + cos x


 tan 2


\[\sin \sqrt{2x}\]


\[\tan \sqrt{x}\] 


\[\frac{x^3}{3} - 2\sqrt{x} + \frac{5}{x^2}\]


\[\frac{1}{\sin x} + 2^{x + 3} + \frac{4}{\log_x 3}\] 


\[If y = \sqrt{\frac{x}{a}} + \sqrt{\frac{a}{x}}, \text{ prove that } 2xy\frac{dy}{dx} = \left( \frac{x}{a} - \frac{a}{x} \right)\]  


xn tan 


(x3 + x2 + 1) sin 


(x sin x + cos x) (x cos x − sin x


(1 − 2 tan x) (5 + 4 sin x)


(1 +x2) cos x


\[\frac{2x - 1}{x^2 + 1}\] 


\[\frac{e^x + \sin x}{1 + \log x}\] 


\[\frac{x \tan x}{\sec x + \tan x}\]


\[\frac{\sqrt{a} + \sqrt{x}}{\sqrt{a} - \sqrt{x}}\] 


\[\frac{1 + \log x}{1 - \log x}\] 


\[\frac{4x + 5 \sin x}{3x + 7 \cos x}\]


If f (1) = 1, f' (1) = 2, then write the value of \[\lim_{x \to 1} \frac{\sqrt{f (x)} - 1}{\sqrt{x} - 1}\] 


Mark the correct alternative in  of the following:

If\[f\left( x \right) = 1 - x + x^2 - x^3 + . . . - x^{99} + x^{100}\]then \[f'\left( 1 \right)\] 


Let f(x) = x – [x]; ∈ R, then f'`(1/2)` is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×