What is the derivative of $f (x) = ln (x^{2} + 2)$ $f(x)=ln (x^2+2)$ ?

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Answer 1 · 2016-07-08T20:50:43

Using the chain rule on $f (x) = ln (x^{2} + 2)$ $f(x) = ln(x^2+2)$ , we let

$u = x^{2} + 2$ $u=x^2+2$ , so $d u = 2 x$ $du=2x$ , so $f'(x) = (2x)/(x^2+2)$ .

We've used the definition $d/dx[ln(u)]=(du)/(u)$ .

What is the derivative of f(x)=ln (x^2+2)f(x)=ln(x2+2)f(x)=ln (x^2+2)?