What is the derivative of ln(arctan(cos(x))) ?

The derivative of ln(arctan(cos(x))) is -(sin(x))/(arctan(cos(x))(cos^2(x)+1))

What is the first derivative of ln(arctan(cos(x))) ?

The first derivative of ln(arctan(cos(x))) is -(sin(x))/(arctan(cos(x))(cos^2(x)+1))

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

- \frac{sin ( x )}{arctan ( cos ( x ) ) ( cos ^{2} ( x ) + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (cos (x))) = - \frac{sin ( x )}{cos ^{2} ( x ) + 1}

= \frac{1}{arctan ( cos ( x ) )} (- \frac{sin ( x )}{cos ^{2} ( x ) + 1})

Simplify

\frac{1}{arctan ( cos ( x ) )} (- \frac{sin ( x )}{cos ^{2} ( x ) + 1}) : - \frac{sin ( x )}{arctan ( cos ( x ) ) ( cos ^{2} ( x ) + 1 )}

= - \frac{sin ( x )}{arctan ( cos ( x ) ) ( cos ^{2} ( x ) + 1 )}

\int cos (x π) d x

\int_{0}^{2 π} cos^{2} (t) d t

y = 2^{x} + x^{2} (- 1 - x)^{x}

\int 2 cos (x) e^{x} d x

\int 10 e^{1 - 5 x} d x

What is the derivative of ln(arctan(cos(x))) ?
The derivative of ln(arctan(cos(x))) is -(sin(x))/(arctan(cos(x))(cos^2(x)+1))
What is the first derivative of ln(arctan(cos(x))) ?
The first derivative of ln(arctan(cos(x))) is -(sin(x))/(arctan(cos(x))(cos^2(x)+1))