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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{( cos ( x ) ) ^{2} + 1} \frac{d}{d x} (cos (x))

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

\frac{d}{d x} (cos (x)) = - sin (x)

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

Simplify

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

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

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