What is the derivative of arctan(cos(7x)) ?

The derivative of arctan(cos(7x)) is -(7sin(7x))/(cos^2(7x)+1)

What is the first derivative of arctan(cos(7x)) ?

The first derivative of arctan(cos(7x)) is -(7sin(7x))/(cos^2(7x)+1)

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derivative of

arctan (cos (7 x))

- \frac{7 sin ( 7 x )}{cos ^{2} ( 7 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (cos (7 x)))

Apply the chain rule:

\frac{1}{( cos ( 7 x ) ) ^{2} + 1} \frac{d}{d x} (cos (7 x))

= \frac{1}{( cos ( 7 x ) ) ^{2} + 1} \frac{d}{d x} (cos (7 x))

\frac{d}{d x} (cos (7 x)) = - sin (7 x) \cdot 7

= \frac{1}{( cos ( 7 x ) ) ^{2} + 1} (- sin (7 x) \cdot 7)

Simplify

\frac{1}{cos ^{2} ( 7 x ) + 1} (- sin (7 x) \cdot 7) : - \frac{7 sin ( 7 x )}{cos ^{2} ( 7 x ) + 1}

= - \frac{7 sin ( 7 x )}{cos ^{2} ( 7 x ) + 1}

x + y + 6

\int_{0}^{8} e^{- 0.25 t} d t

\int sin (3 x) sin (6 x) d x

[x^{2} (x^{2} + 8 x)]^{6}

x^{2} \frac{d y}{d x} = y^{2}

What is the derivative of arctan(cos(7x)) ?
The derivative of arctan(cos(7x)) is -(7sin(7x))/(cos^2(7x)+1)
What is the first derivative of arctan(cos(7x)) ?
The first derivative of arctan(cos(7x)) is -(7sin(7x))/(cos^2(7x)+1)