Advertisement Remove all ads

Xn Loga X - Mathematics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

xn loga 

Advertisement Remove all ads

Solution

\[\text{ Let } u = x^n ; v = \log_a x = \frac{\log x}{\log a}\]
\[\text{ Then }, u' = n x^{n - 1} ; v' = \frac{1}{x \log a}\]
\[\text{ Using the product rule }:\]
\[\frac{d}{dx}\left( uv \right) = uv' + vu'\]
\[\frac{d}{dx}\left( x^n \log_a x \right) = x^n . \frac{1}{x \log a} + \log_a x \left( n x^{n - 1} \right)\]
\[ = x^{n - 1} \frac{1}{\log a} + \log_a x \left( n x^{n - 1} \right)\]
\[ = x^{n - 1} \left( \frac{1}{\log a} + n \log_a x \right)\]

Concept: The Concept of Derivative - Algebra of Derivative of Functions
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Exercise 30.4 | Q 5 | Page 39

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×