what is the derivative of....?

Question

f(x)=(x^2 +16x +164 +6400x^-2 +1600x^-1)^(1/2)

Answer 1

Use the product and power rules:

If f(x) = g(h(x)), then

f'(x)= g'(h(x))*h'(x)

In your case h(x) = x^2 +16x +164 +6400x^-2 +1600x^-1
And g(x) = (h(x))^(1/2)

From there, just start taking derivatives according to the power rule.

Answer 2

df/dx = (2x+16 -12800/x^3 - 1600/x^2)/[2*sqrt(x^2 + 16x +6400/x^2+1600/x)]