en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of cos(arctan(3x))

Solution

\frac{d}{d x} (cos (arctan (3 x)))

Solution

- \frac{9 x}{( 9 x ^{2} + 1 ) 1 + 9 x ^{2}}

Solution steps

\frac{d}{d x} (cos (arctan (3 x)))

Apply the chain rule:

- sin (arctan (3 x)) \frac{d}{d x} (arctan (3 x))

= - sin (arctan (3 x)) \frac{d}{d x} (arctan (3 x))

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= - sin (arctan (3 x)) \frac{3}{9 x ^{2} + 1}

Simplify

- sin (arctan (3 x)) \frac{3}{9 x ^{2} + 1} : - \frac{9 x}{( 9 x ^{2} + 1 ) 1 + 9 x ^{2}}

= - \frac{9 x}{( 9 x ^{2} + 1 ) 1 + 9 x ^{2}}

Popular Examples

integral from 0 to 1/10 of xln(10x)

\int_{0}^{\frac{1}{10}} x ln (10 x) d x

limit as x approaches 0 of sqrt(2)

x \to 0 lim (2)

tangent of f(x)=3tan(x),\at x= pi/3 tangent of

f (x) = 3 tan (x), at x = \frac{π}{3}

integral from-infinity to 0 of x

\int_{- \infty}^{0} x d x

1/2*(dy)/(dx)=(2x)/(3y)

\frac{1}{2} \cdot \frac{d y}{d x} = \frac{2 x}{3 y}

Frequently Asked Questions (FAQ)

What is the derivative of cos(arctan(3x)) ?
The derivative of cos(arctan(3x)) is -(9x)/((9x^2+1)sqrt(1+9x^2))
What is the first derivative of cos(arctan(3x)) ?
The first derivative of cos(arctan(3x)) is -(9x)/((9x^2+1)sqrt(1+9x^2))