These four are a table to learn rather than a rule to apply, and then the chain rule does the rest. The square in the denominator is where the multiple inside ends up.
The derivative of inverse tangent is one over one plus the inside squared.
The inside is 3x, so its square is 9x squared, and its derivative is 3.
So the answer is 3 over 1 plus 9x squared.
The answer is 1+9x23.
Where students go wrong
Squaring only the x. The whole inside gets squared, so 3x becomes 9x squared, and losing the 9 is the mistake that survives all the way to the answer looking plausible.
Also called arcsin derivative, arctan derivative, inverse sine derivative or derivative of tan inverse.
Questions about these worksheets
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That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the derivatives of inverse trig functions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
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Squaring only the x. The whole inside gets squared, so 3x becomes 9x squared, and losing the 9 is the mistake that survives all the way to the answer looking plausible.