What is the derivative of arctan(cos(8x)) ?

The derivative of arctan(cos(8x)) is -(8sin(8x))/(cos^2(8x)+1)

What is the first derivative of arctan(cos(8x)) ?

The first derivative of arctan(cos(8x)) is -(8sin(8x))/(cos^2(8x)+1)

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\frac{d}{d x} (arctan (cos (8 x)))

- \frac{8 sin ( 8 x )}{cos ^{2} ( 8 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (cos (8 x)))

Apply the chain rule:

\frac{1}{( cos ( 8 x ) ) ^{2} + 1} \frac{d}{d x} (cos (8 x))

= \frac{1}{( cos ( 8 x ) ) ^{2} + 1} \frac{d}{d x} (cos (8 x))

\frac{d}{d x} (cos (8 x)) = - sin (8 x) \cdot 8

= \frac{1}{( cos ( 8 x ) ) ^{2} + 1} (- sin (8 x) \cdot 8)

Simplify

\frac{1}{cos ^{2} ( 8 x ) + 1} (- sin (8 x) \cdot 8) : - \frac{8 sin ( 8 x )}{cos ^{2} ( 8 x ) + 1}

= - \frac{8 sin ( 8 x )}{cos ^{2} ( 8 x ) + 1}

\frac{d}{d x} (x e^{- k x})

\int_{1}^{\infty} 5^{- x} d x

x \to 1 lim (e^{6 x^{3} - 6 x})

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

x^{2} - x - 2, 3

What is the derivative of arctan(cos(8x)) ?
The derivative of arctan(cos(8x)) is -(8sin(8x))/(cos^2(8x)+1)
What is the first derivative of arctan(cos(8x)) ?
The first derivative of arctan(cos(8x)) is -(8sin(8x))/(cos^2(8x)+1)