en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of y=arctan(cos(x))

Solution

derivative of

y = arctan (cos (x))

Solution

- \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}

Popular Examples

derivative of e^{2x}+x^3

\frac{d}{d x} (e^{2 x} + x^{3})

(\partial)/(\partial y)(2x^3y+cos(x^2))

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

derivative of Ce^{3x}

\frac{d}{d x} (C e^{3 x})

integral of 1/((x-1)(x-3)(x+4))

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

(sqrt(9-x^2))^'

(9 - x^{2})^{^{'}}

Frequently Asked Questions (FAQ)

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