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

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

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

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

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derivative of

arctan (cos (θ))

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

Solution steps

\frac{d}{d θ} (arctan (cos (θ)))

Apply the chain rule:

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

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

\frac{d}{d θ} (cos (θ)) = - sin (θ)

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

Simplify

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

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

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