What is the derivative of y=ln(arctan(4x)) ?

The derivative of y=ln(arctan(4x)) is 4/(arctan(4x)(16x^2+1))

What is the first derivative of y=ln(arctan(4x)) ?

The first derivative of y=ln(arctan(4x)) is 4/(arctan(4x)(16x^2+1))

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derivative of

y = ln (arctan (4 x))

\frac{4}{arctan ( 4 x ) ( 16 x ^{2} + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= \frac{1}{arctan ( 4 x )} \cdot \frac{4}{16 x ^{2} + 1}

Simplify

\frac{1}{arctan ( 4 x )} \cdot \frac{4}{16 x ^{2} + 1} : \frac{4}{arctan ( 4 x ) ( 16 x ^{2} + 1 )}

= \frac{4}{arctan ( 4 x ) ( 16 x ^{2} + 1 )}

\int_{1}^{3} 5 r^{3} ln (r) d r

y^{^{''}} - y^{^{'}} - 2 y = 2 e^{- t}

\int tan^{3} (x) sec^{\frac{1}{2}} (x) d x

x \to 0 lim (\frac{1}{e ^{x}})

x \to 6 lim (\frac{x}{x ^{2} - 36})

What is the derivative of y=ln(arctan(4x)) ?
The derivative of y=ln(arctan(4x)) is 4/(arctan(4x)(16x^2+1))
What is the first derivative of y=ln(arctan(4x)) ?
The first derivative of y=ln(arctan(4x)) is 4/(arctan(4x)(16x^2+1))