What is the derivative of arctan(sqrt(2x^3)) ?

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

What is the first derivative of arctan(sqrt(2x^3)) ?

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

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

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

Solution steps

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

Simplify

arctan (2 x^{3}) : arctan (2 x^{3})

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{( 5 x + 7 )}{x ^{2} + 4 x + 4} d x

\frac{d}{d x} (10000 - 9000 e^{- 0.3 x})

\frac{d}{d x} (\frac{x ^{2}}{e ^{3 - 4 x}})

\frac{9}{sin ( x ) + cos ( x )}

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