What is the derivative of arctan(sqrt(x^3)) ?

The derivative of arctan(sqrt(x^3)) is (3sqrt(x))/(2(x^3+1))

What is the first derivative of arctan(sqrt(x^3)) ?

The first derivative of arctan(sqrt(x^3)) is (3sqrt(x))/(2(x^3+1))

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\frac{d}{d x} (arctan (x^{3}))

\frac{3 x}{2 ( x ^{3} + 1 )}

Solution steps

\frac{d}{d x} (arctan (x^{3}))

Apply the chain rule:

\frac{1}{( x ^{3} ) ^{2} + 1} \frac{d}{d x} (x^{3})

= \frac{1}{( x ^{3} ) ^{2} + 1} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = \frac{3 x}{2}

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

Simplify

\frac{1}{( x ^{3} ) ^{2} + 1} \cdot \frac{3 x}{2} : \frac{3 x}{2 ( x ^{3} + 1 )}

= \frac{3 x}{2 ( x ^{3} + 1 )}

What is the derivative of arctan(sqrt(x^3)) ?
The derivative of arctan(sqrt(x^3)) is (3sqrt(x))/(2(x^3+1))
What is the first derivative of arctan(sqrt(x^3)) ?
The first derivative of arctan(sqrt(x^3)) is (3sqrt(x))/(2(x^3+1))