Differentiation Question 234
Question: $ \frac{d}{dx}( x^{3}{{\tan }^{2}}\frac{x}{2} ) $ =
[AISSE 1979]
Options:
A) $ x^{3}\tan \frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3x{{\tan }^{2}}\frac{x}{2} $
B) $ x^{3}\tan \frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3x^{2}{{\tan }^{2}}\frac{x}{2} $
C) $ x^{3}{{\tan }^{2}}\frac{x}{2}.{{\sec }^{2}}\frac{x}{2}+3x^{2}{{\tan }^{2}}\frac{x}{2} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{d}{dx}( x^{3}{{\tan }^{2}}\frac{x}{2} )=3x^{2}{{\tan }^{2}}\frac{x}{2}+2x^{3}\tan \frac{x}{2}{{\sec }^{2}}\frac{x}{2}.\frac{1}{2} $
$ =x^{3}\tan \frac{x}{2}{{\sec }^{2}}\frac{x}{2}+3x^{2}{{\tan }^{2}}\frac{x}{2} $ .
BETA
