What is the derivative of ln(arctan(2x^5)) ?

The derivative of ln(arctan(2x^5)) is (10x^4)/(arctan(2x^5)(4x^{10)+1)}

What is the first derivative of ln(arctan(2x^5)) ?

The first derivative of ln(arctan(2x^5)) is (10x^4)/(arctan(2x^5)(4x^{10)+1)}

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\frac{d}{d x} (ln (arctan (2 x^{5})))

\frac{10 x ^{4}}{arctan ( 2 x ^{5} ) ( 4 x ^{10} + 1 )}

Solution steps

\frac{d}{d x} (ln (arctan (2 x^{5})))

Apply the chain rule:

\frac{1}{arctan ( 2 x ^{5} )} \frac{d}{d x} (arctan (2 x^{5}))

= \frac{1}{arctan ( 2 x ^{5} )} \frac{d}{d x} (arctan (2 x^{5}))

\frac{d}{d x} (arctan (2 x^{5})) = \frac{10 x ^{4}}{4 x ^{10} + 1}

= \frac{1}{arctan ( 2 x ^{5} )} \cdot \frac{10 x ^{4}}{4 x ^{10} + 1}

Simplify

\frac{1}{arctan ( 2 x ^{5} )} \cdot \frac{10 x ^{4}}{4 x ^{10} + 1} : \frac{10 x ^{4}}{arctan ( 2 x ^{5} ) ( 4 x ^{10} + 1 )}

= \frac{10 x ^{4}}{arctan ( 2 x ^{5} ) ( 4 x ^{10} + 1 )}

\int \frac{1}{6 x ^{5}} d x

3 \cdot 2^{2 x + 1}

\int_{0}^{1} r 1 - r^{2} d r

\int (\frac{x ^{3}}{x - 1}) d x

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

What is the derivative of ln(arctan(2x^5)) ?
The derivative of ln(arctan(2x^5)) is (10x^4)/(arctan(2x^5)(4x^{10)+1)}
What is the first derivative of ln(arctan(2x^5)) ?
The first derivative of ln(arctan(2x^5)) is (10x^4)/(arctan(2x^5)(4x^{10)+1)}