English

Find the derivative of x2 cosx.

Advertisements
Advertisements

Question

Find the derivative of x2 cosx.

Sum
Advertisements

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

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the derivative of x at x = 1.


Find the derivative of x–4 (3 – 4x–5).


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):

(x + a)


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)/(cx + d)`


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):

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


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):

sinn x


Find the derivative of f (x) x at x = 1

 


Find the derivative of f (x) = cos x at x = 0


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


k xn


\[\sqrt{2 x^2 + 1}\]


Differentiate each of the following from first principle:

\[\frac{\sin x}{x}\]


Differentiate each of the following from first principle:

\[e^\sqrt{ax + b}\]


Differentiate each of the following from first principle:

\[a^\sqrt{x}\]


Differentiate each of the following from first principle:

\[3^{x^2}\]


tan2 x 


\[\text{ If } y = \left( \sin\frac{x}{2} + \cos\frac{x}{2} \right)^2 , \text{ find } \frac{dy}{dx} at x = \frac{\pi}{6} .\]


For the function \[f(x) = \frac{x^{100}}{100} + \frac{x^{99}}{99} + . . . + \frac{x^2}{2} + x + 1 .\]

 

x3 ex 


xn tan x 


xn loga x 


sin2 x 


\[e^x \log \sqrt{x} \tan x\] 


(ax + b)n (cx + d)n 


\[\frac{x^2 + 1}{x + 1}\] 


\[\frac{e^x - \tan x}{\cot x - x^n}\] 


\[\frac{1}{a x^2 + bx + c}\] 


\[\frac{e^x + \sin x}{1 + \log x}\] 


\[\frac{\sin x - x \cos x}{x \sin x + \cos x}\]


\[\frac{a + \sin x}{1 + a \sin x}\] 


\[\frac{1 + \log x}{1 - \log x}\] 


\[\frac{p x^2 + qx + r}{ax + b}\]


Write the value of the derivative of f (x) = |x − 1| + |x − 3| at x = 2.


Mark the correct alternative in of the following: 

If \[f\left( x \right) = \frac{x - 4}{2\sqrt{x}}\]

 


Mark the correct alternative in of the following:

If\[y = 1 + \frac{x}{1!} + \frac{x^2}{2!} + \frac{x^3}{3!} + . . .\]then \[\frac{dy}{dx} =\] 

 


`(a + b sin x)/(c + d cos x)`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×