# Question #83ab4

##### 2 Answers

Yes, this is true. See the explanation below...

#### Explanation:

This answer many not be as formal as a proper mathematical proof, but I hope it will do.

According to the chain rule, when we differentiate

When we differentiate a second time. the process repeats itself, as the differentiation of the exponential yields another factor of 2:

(In truth, this is an application of the product rule, but I have omitted the second term, as the derivative of 2 is zero.)

This pattern continues for as many times as you choose to do the differentiation. Each derivative places another factor of 2 in front of the result, so that after

Use an inductive proof.

Assume that

Then differentiate again:

So **if** it is true for **must** be true for

Next as we are in