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Popular >

derivative of arctan(cos(x))

Solution

derivative of

arctan (cos (x))

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of (2x^2-24)/(x(x+2)^3)

\int \frac{2 x ^{2} - 24}{x ( x + 2 ) ^{3}} d x

integral of ((x-2)^n)/n

\int \frac{( x - 2 ) ^{n}}{n} d x

derivative of (sqrt(x)/(2x-7))

\frac{d}{d x} (\frac{x}{2 x - 7})

integral from 9 to 25 of (sqrt(x-9))/x

\int_{9}^{25} \frac{x - 9}{x} d x

(cos(x)+ysin(x))dx+(cos(x))dy=0

(cos (x) + y sin (x)) d x + (cos (x)) d y = 0

Frequently Asked Questions (FAQ)

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