Question #1590c

1 Answer
Jan 9, 2018

x/sqrt(1+x^2)

Explanation:

Your original function is

y=sqrt(1+x^2)

For simplicity, I will rewrite this as the following

y=(1+x^2)^(1/2)

So this uses a chain rule and a power rule. The chain rule says the following:

d/dx(f(g(x)))=f'(g(x))*g'(x)

In this case, we can make the observation that

f(x)=x^(1/2)

and

g(x) = 1+x^2

So now we need to take the derivative of each:

f'(x)=d/dx(x^(1/2))

f'(x)=1/(2sqrt(x))

g'(x)=d/dx(1+x^2)

g'(x)=2x

So now we can finish the chain rule using the logic mentioned above that

d/dx(f(g(x)))=f'(g(x))*g'(x)

to get the final answer

x/sqrt(1+x^2)