What is the derivative of arctan(9x^4) ?

The derivative of arctan(9x^4) is (36x^3)/(81x^8+1)

What is the first derivative of arctan(9x^4) ?

The first derivative of arctan(9x^4) is (36x^3)/(81x^8+1)

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derivative of

arctan (9 x^{4})

\frac{36 x ^{3}}{81 x ^{8} + 1}

Solution steps

\frac{d}{d x} (arctan (9 x^{4}))

Apply the chain rule:

\frac{1}{( 9 x ^{4} ) ^{2} + 1} \frac{d}{d x} (9 x^{4})

= \frac{1}{( 9 x ^{4} ) ^{2} + 1} \frac{d}{d x} (9 x^{4})

\frac{d}{d x} (9 x^{4}) = 36 x^{3}

= \frac{1}{( 9 x ^{4} ) ^{2} + 1} \cdot 36 x^{3}

Simplify

\frac{1}{( 9 x ^{4} ) ^{2} + 1} \cdot 36 x^{3} : \frac{36 x ^{3}}{81 x ^{8} + 1}

= \frac{36 x ^{3}}{81 x ^{8} + 1}

What is the derivative of arctan(9x^4) ?
The derivative of arctan(9x^4) is (36x^3)/(81x^8+1)
What is the first derivative of arctan(9x^4) ?
The first derivative of arctan(9x^4) is (36x^3)/(81x^8+1)