What is the derivative of ln(arctan(8x^5)) ?

The derivative of ln(arctan(8x^5)) is (40x^4)/(arctan(8x^5)(64x^{10)+1)}

What is the first derivative of ln(arctan(8x^5)) ?

The first derivative of ln(arctan(8x^5)) is (40x^4)/(arctan(8x^5)(64x^{10)+1)}

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\frac{d}{d x} (ln (arctan (8 x^{5})))

\frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

Solution steps

\frac{d}{d x} (ln (arctan (8 x^{5})))

Apply the chain rule:

\frac{1}{arctan ( 8 x ^{5} )} \frac{d}{d x} (arctan (8 x^{5}))

= \frac{1}{arctan ( 8 x ^{5} )} \frac{d}{d x} (arctan (8 x^{5}))

\frac{d}{d x} (arctan (8 x^{5})) = \frac{40 x ^{4}}{64 x ^{10} + 1}

= \frac{1}{arctan ( 8 x ^{5} )} \cdot \frac{40 x ^{4}}{64 x ^{10} + 1}

Simplify

\frac{1}{arctan ( 8 x ^{5} )} \cdot \frac{40 x ^{4}}{64 x ^{10} + 1} : \frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

= \frac{40 x ^{4}}{arctan ( 8 x ^{5} ) ( 64 x ^{10} + 1 )}

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

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

(1 + y^{2} + x y^{2}) d x + (x^{2} y + y + 2 x y) d y = 0

\frac{d}{d x} (x^{0.6})

y = x, y = 12 x, x = 9

What is the derivative of ln(arctan(8x^5)) ?
The derivative of ln(arctan(8x^5)) is (40x^4)/(arctan(8x^5)(64x^{10)+1)}
What is the first derivative of ln(arctan(8x^5)) ?
The first derivative of ln(arctan(8x^5)) is (40x^4)/(arctan(8x^5)(64x^{10)+1)}