What is the (arctan(cos(x)))^' ?

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

What is the first (arctan(cos(x)))^' ?

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

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(arctan (cos (x)))^{^{'}}

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

Solution steps

(arctan (cos (x)))^{'}

Apply the chain rule:

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

= \frac{1}{( cos ( x ) ) ^{2} + 1} (cos (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 (arctan(cos(x)))^' ?
The (arctan(cos(x)))^' is -(sin(x))/(cos^2(x)+1)
What is the first (arctan(cos(x)))^' ?
The first (arctan(cos(x)))^' is -(sin(x))/(cos^2(x)+1)