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))

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

- \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}}

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

x \to 0 lim (2)

f (x) = 3 tan (x), at x = \frac{π}{3}

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

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

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))