How do you find the derivative of f(x)=sqrt(a^2+x^2)?

1 Answer
Sep 17, 2016

f'(x) = x/(sqrt(a^2+x^2))

Explanation:

The chain rule goes like this:
If f(x) =(g(x))^n, then f'(x)=n(g(x))^(n-1)*d/dxg(x)

Applying this rule:

f(x) = sqrt(a^2+x^2)= (a^2+x^2)^(1/2)

f'(x) = 1/2(a^2+x^2)^(1/2-1) * d/dx(a^2+x^2)

f'(x) = 1/2(a^2+x^2)^(-1/2) * 2x

f'(x) = 1/(2(a^2+x^2)^(1/2))*2x

f'(x) = x/((a^2+x^2)^(1/2))

f'(x) = x/(sqrt(a^2+x^2))