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Numerade Educator

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Problem 46 Medium Difficulty

Show that $ \frac {d}{dx} \sqrt[4]{ \frac {1 + \tanh x}{1 - \tanh x}} = \frac {1}{2} e^{x/2}. $

Answer

$\frac{1}{2} e^{\frac{x}{2}}$

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Video Transcript

we know that sign h of X over coastline Ajax either the ex minister to the night of axe over each of the AKs, possibly to the negative axe gives us the four through of one plus tangent. A jukebox over one minus tangent. H rocks gives us the four through of to eat of the axe over to eat of the negative axe. Obviously, we can cancel out the twos. The 4th 3rd of each of the two acts equals e the 1/2 acts using the chain rule Eat of the X over two times 1/2. Remember, the derivative of X over two is 1/2 gives us 1/2 eat of the X over too.