What is the derivative of cos(arctan(6x)) ?

The derivative of cos(arctan(6x)) is -(36x)/((36x^2+1)sqrt(1+36x^2))

What is the first derivative of cos(arctan(6x)) ?

The first derivative of cos(arctan(6x)) is -(36x)/((36x^2+1)sqrt(1+36x^2))

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\frac{d}{d x} (cos (arctan (6 x)))

- \frac{36 x}{( 36 x ^{2} + 1 ) 1 + 36 x ^{2}}

Solution steps

\frac{d}{d x} (cos (arctan (6 x)))

Apply the chain rule:

- sin (arctan (6 x)) \frac{d}{d x} (arctan (6 x))

= - sin (arctan (6 x)) \frac{d}{d x} (arctan (6 x))

\frac{d}{d x} (arctan (6 x)) = \frac{6}{36 x ^{2} + 1}

= - sin (arctan (6 x)) \frac{6}{36 x ^{2} + 1}

Simplify

- sin (arctan (6 x)) \frac{6}{36 x ^{2} + 1} : - \frac{36 x}{( 36 x ^{2} + 1 ) 1 + 36 x ^{2}}

= - \frac{36 x}{( 36 x ^{2} + 1 ) 1 + 36 x ^{2}}

\frac{d}{d x} (x^{4} (7 - x^{2})^{3})

\int arctan (tan (x)) d x

\int \frac{45}{1 - cos ( 5 x )} d x

- 4

f (- 1) = - x^{3}

What is the derivative of cos(arctan(6x)) ?
The derivative of cos(arctan(6x)) is -(36x)/((36x^2+1)sqrt(1+36x^2))
What is the first derivative of cos(arctan(6x)) ?
The first derivative of cos(arctan(6x)) is -(36x)/((36x^2+1)sqrt(1+36x^2))