Скачать или смотреть How to use the chain rule: derivative of sqrt(x^2+2)

When we take the derivative of a function composition, the chain rule says to differentiate with respect to the inner function (treating it as a single variable), then tack on the derivative OF the inner function.

In this chain rule derivative review, we differentiate sqrt(x^2+2) using the chain rule, so we start by differentiating with respect to the interior function x^2+2. It's helpful to express our function with a fractional exponent as (x^2+2)^(1/2) to make it clear how to use the power rule for this first step, which gives us 1/2*(x^2+2)^(-1/2).

Finally, we just have to tack on the derivative of the inner function, which is 2x, and we simplify the final answer to x/sqrt(x^2+2).