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derivative of arctan(cos(θ))

Solution

derivative of

arctan (cos (θ))

Solution

- \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}

Popular Examples

implicit (dy}{dx},y=\frac{-5x)/5+3sqrt(x^3)-4/(5sqrt(x))implicit derivative

\frac{d y}{d x}, y = \frac{- 5 x}{5} + 3 x^{3} - \frac{4}{5 x}

tangent of y=3x^2-5x+9 tangent of

y = 3 x^{2} - 5 x + 9

y^{''}+9y=3sec(3x)

y^{^{''}} + 9 y = 3 sec (3 x)

derivative of 5xe^{2x}derivative of

5 x e^{2 x}

derivative of (x^2/(sqrt(4-x^2-y^2)))

\frac{d}{d x} (\frac{x ^{2}}{4 - x ^{2} - y ^{2}})

Frequently Asked Questions (FAQ)

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)