Differentiate with respect to x: F(x)=(x^2+1)^2

To differentiate composite functions, (a function within a function) like in this case we need to use the chain rule. We can see that F(x)=f(g(x)) where we let f(x)= (x^2+1)^2 and g(x)= x^2+1. To use the chain rule we need to find f'(x) and g'(x). The derivative of both functions. To find the derivative of f(x) we let u= x^2+1 so f(u) becomes: u^2 so when we differentiate it we get f'(u)= 2u. Now we substitute u back in. So f'(x)=2(x^2+1). And g'(x)= 2x, we just differentiate it normally. Now we put it all together, the chain rule says: F'(x)= f'(g(x))g'(x) so F'(x)= 2(x^2+1)2x = 4x(x^2+1)