What is the derivative of arctan(x^{10}) ?

The derivative of arctan(x^{10}) is (10x^9)/(x^{20)+1}

What is the first derivative of arctan(x^{10}) ?

The first derivative of arctan(x^{10}) is (10x^9)/(x^{20)+1}

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derivative of

arctan (x^{10})

\frac{10 x ^{9}}{x ^{20} + 1}

Solution steps

\frac{d}{d x} (arctan (x^{10}))

Apply the chain rule:

\frac{1}{( x ^{10} ) ^{2} + 1} \frac{d}{d x} (x^{10})

= \frac{1}{( x ^{10} ) ^{2} + 1} \frac{d}{d x} (x^{10})

\frac{d}{d x} (x^{10}) = 10 x^{9}

= \frac{1}{( x ^{10} ) ^{2} + 1} \cdot 10 x^{9}

Simplify

\frac{1}{( x ^{10} ) ^{2} + 1} \cdot 10 x^{9} : \frac{10 x ^{9}}{x ^{20} + 1}

= \frac{10 x ^{9}}{x ^{20} + 1}

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What is the derivative of arctan(x^{10}) ?
The derivative of arctan(x^{10}) is (10x^9)/(x^{20)+1}
What is the first derivative of arctan(x^{10}) ?
The first derivative of arctan(x^{10}) is (10x^9)/(x^{20)+1}