'Chain' Rule Of Factorials

Calculus Level 1

If $y = 1 + x +\dfrac{x^2}{2!} +\dfrac{x^3}{3!} + \dfrac{x^4}{4!} + ...$ , find $\dfrac {dy}{dx}$ .

\infty

2!

1!

Infinitely long functions are not differentiable

99!

Same as the original function

1!+2!+3!+\cdots+99!

1 solution

Arkajyoti Banerjee
Apr 22, 2016

Looking forward to differentiate $y$ ,

Therefore, its derivative is equal to the original function itself.

Question source: Derivatives - Example 2 - Mathematics For Class XI, R. D. Sharma (Pg 30.30)

Obviously this is the expansion serious of $e^x$ whose derivative is the function itself... Its good that you mentioned the source of question... Cheers.. (+1)

Rishabh Jain - 5 years, 1 month ago

Exactly, this is reason why $e^{x}$ is one of my favourite functions :)

Arkajyoti Banerjee - 5 years, 1 month ago

This is a very easy sum .

Md Zuhair - 4 years, 9 months ago

I know. That's why it is rated a Level 1 in Calculus.

Arkajyoti Banerjee - 4 years, 9 months ago

Oh... Your Name looks like you are a Bangali... I am a bangali too.

Md Zuhair - 4 years, 9 months ago

@Md Zuhair – Ah yeah I'm a bengali.

Arkajyoti Banerjee - 4 years, 9 months ago

@Arkajyoti Banerjee – Ar ei onko ta SN De 'r onko na?? If you know it :P

Md Zuhair - 4 years, 9 months ago

@Md Zuhair – See the last line of the solution. It is not from Sourendranath De's book ;)

Arkajyoti Banerjee - 4 years, 9 months ago

'Chain' Rule Of Factorials

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