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Calculus Level 1

What is the 201 4 th 2014^{\text{th} } derivative of tan ⁡ ( x ) \tan (x) at x = 0 x = 0 ?


The answer is 0.

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Shikhar Jaiswal
Mar 25, 2014

Infinite Expansion of tan ⁡ ( x ) = x + ( x 3 3 ) + ( 2 x 5 15 ) + . . . . . . \tan(x)=x+(\frac {x^3}{3})+(\frac {2x^5}{15})+......

Clearly...the expansion consists of only odd powers of x and on differentiating 2014 times there will be terms which will have odd powers of x x and at x = 0 x=0 all these terms will be equal to zero so answer is: 0 \boxed{0}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

While this is a good way of understanding the answer, you actually need to find f ( n ) ( x ) f^{(n) } (x) in order to calculate the infinite expansion. So this is likely a circular argument.

Calvin Lin Staff - 7 years, 2 months ago
Samarth Sangam
Aug 22, 2014

In 2014th derivative of tanx there is at least one tanx in each terms and 2014th derivative at x=0, tanx=0 when x=0 therefore 2014th derivative of tanx is 0

4 Helpful 0 Interesting 0 Brilliant 0 Confused

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