# What is the second derivative of #(f * g)(x)# if f and g are functions such that #f'(x)=g(x)# and #g'(x)=f(x)#?

##### 2 Answers

Mar 19, 2018

#### Explanation:

Let

Then using the product rule:

Using the condition given in the question, we get:

Now using the power and chain rules:

Applying the special condition of this question again, we write:

Mar 19, 2018

Another answer in case

#### Explanation:

We want to find the second derivative of

We differentiate once using the chain rule.

Then we differentiate again using the product chain rules