Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

Tan 2x - Mathematics

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

 tan 2

Advertisement Remove all ads

Solution

\[ \frac{d}{dx}\left( f(x) \right) = \lim_{h \to 0} \frac{f\left( x + h \right) - f\left( x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\tan \left( 2x + 2h \right) - \tan \left( 2x \right)}{h}\]
\[ = \lim_{h \to 0} \frac{\frac{sin \left( 2x + 2h \right)}{\cos \left( 2x + 2h \right)} - \frac{\sin \left( 2x \right)}{\cos \left( 2x \right)}}{h}\]
\[ = \lim_{h \to 0} \frac{sin \left( 2x + 2h \right) \cos \left( 2x \right) - \cos \left( 2x + 2h \right) \sin \left( 2x \right)}{h \cos \left( 2x + 2h \right) \cos \left( 2x \right)}\]
\[ = \lim_{h \to 0} \frac{\sin \left( 2x + 2h - 2x \right)}{h \cos \left( 2x + 2h \right) \cos \left( 2x \right)}\]
\[ = \frac{1}{\cos 2x} \lim_{h \to 0} \frac{\sin \left( 2h \right)}{2h} \times 2 \times \lim_{h \to 0} \frac{1}{\cos \left( 2x + 2h \right)}\]
\[ = \frac{1}{\cos 2x} \times 2 \times \frac{1}{\cos 2x}\]
\[ = \frac{2}{\cos^2 \left( 2x \right)}\]
\[ = 2 \sec^2 \left( 2x \right)\]

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 30.2 | Q 4.3 | Page 26

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×