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)#?
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:
Another answer in case
We want to find the second derivative of
We differentiate once using the chain rule.
Then we differentiate again using the product chain rules