What is the derivative of arctan(cos(3x)) ?

The derivative of arctan(cos(3x)) is -(3sin(3x))/(cos^2(3x)+1)

What is the first derivative of arctan(cos(3x)) ?

The first derivative of arctan(cos(3x)) is -(3sin(3x))/(cos^2(3x)+1)

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derivative of

arctan (cos (3 x))

- \frac{3 sin ( 3 x )}{cos ^{2} ( 3 x ) + 1}

Solution steps

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

Apply the chain rule:

\frac{1}{( cos ( 3 x ) ) ^{2} + 1} \frac{d}{d x} (cos (3 x))

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

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

= \frac{1}{( cos ( 3 x ) ) ^{2} + 1} (- sin (3 x) \cdot 3)

Simplify

\frac{1}{cos ^{2} ( 3 x ) + 1} (- sin (3 x) \cdot 3) : - \frac{3 sin ( 3 x )}{cos ^{2} ( 3 x ) + 1}

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

\int \frac{x - 1}{x ^{3}} d x

f (y) = 2 e^{y}

x \to - 4 lim (\frac{\frac{4}{x} + 1}{x + 4})

\int_{0}^{1} 1 + (- 2 x)^{2} d x

f (x) = x^{2} + 5, (3, 14)

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