What is the derivative of ln(arctan(5x^4)) ?

The derivative of ln(arctan(5x^4)) is (20x^3)/(arctan(5x^4)(25x^8+1))

What is the first derivative of ln(arctan(5x^4)) ?

The first derivative of ln(arctan(5x^4)) is (20x^3)/(arctan(5x^4)(25x^8+1))

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\frac{d}{d x} (ln (arctan (5 x^{4})))

\frac{20 x ^{3}}{arctan ( 5 x ^{4} ) ( 25 x ^{8} + 1 )}

Solution steps

\frac{d}{d x} (ln (arctan (5 x^{4})))

Apply the chain rule:

\frac{1}{arctan ( 5 x ^{4} )} \frac{d}{d x} (arctan (5 x^{4}))

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

\frac{d}{d x} (arctan (5 x^{4})) = \frac{20 x ^{3}}{25 x ^{8} + 1}

= \frac{1}{arctan ( 5 x ^{4} )} \cdot \frac{20 x ^{3}}{25 x ^{8} + 1}

Simplify

\frac{1}{arctan ( 5 x ^{4} )} \cdot \frac{20 x ^{3}}{25 x ^{8} + 1} : \frac{20 x ^{3}}{arctan ( 5 x ^{4} ) ( 25 x ^{8} + 1 )}

= \frac{20 x ^{3}}{arctan ( 5 x ^{4} ) ( 25 x ^{8} + 1 )}

What is the derivative of ln(arctan(5x^4)) ?
The derivative of ln(arctan(5x^4)) is (20x^3)/(arctan(5x^4)(25x^8+1))
What is the first derivative of ln(arctan(5x^4)) ?
The first derivative of ln(arctan(5x^4)) is (20x^3)/(arctan(5x^4)(25x^8+1))