Compute the derivative of (x+1)^1/2 – log(1+(x+1)^1/2)

by RoRi

November 2, 2015

Compute the derivative of

$f(x) = \sqrt{x+1} - \log \left( 1 + \sqrt{x+1} \right).$

Using the chain rule we can directly compute,

$\begin{align*} f'(x) &= \frac{1}{2\sqrt{x+1}} - \left(\frac{1}{1+\sqrt{x+1}}\right)\left(\frac{1}{2\sqrt{x+1}} \right)\\ &= \left( \frac{1}{2\sqrt{x+1}} \right) \left(1 - \frac{1}{1+\sqrt{x+1}} \right) \\ &= \frac{1}{2\left(1+\sqrt{x+1}\right)}. \end{align*}$

Stumbling Robot

Compute the derivative of (x+1)^1/2 – log(1+(x+1)^1/2)

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