What is (\partial)/(\partial x)(arctan(cos(x))) ?

The answer to (\partial)/(\partial x)(arctan(cos(x))) is -(sin(x))/(cos^2(x)+1)

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(\partial)/(\partial x)(arctan(cos(x)))

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

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

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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}

\frac{\partial}{\partial y} (3 (x - y) e^{3 y + 2 x^{2}})

\frac{d y}{d x} = 0.5 y - 450

2 x cos (x)

\int \frac{1}{4 + ( x - 3 ) ^{2}} d x

x^{2}, x + 2

What is (\partial)/(\partial x)(arctan(cos(x))) ?
The answer to (\partial)/(\partial x)(arctan(cos(x))) is -(sin(x))/(cos^2(x)+1)