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Popular >

derivative of arctan(cos(x))

Solution

\frac{d}{d x} (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 from 7 to 14 of 1/((x-9)^2)

\int_{7}^{14} \frac{1}{( x - 9 ) ^{2}} d x

integral from 0 to 4 of |3t-8|

\int_{0}^{4} ∣ 3 t - 8 ∣ d t

derivative of f(x)=(4x^2-x+3)/(sqrt(x))derivative of

f (x) = \frac{4 x ^{2} - x + 3}{x}

integral of (e^{-st})/(-s)

\int \frac{e ^{- s t}}{- s} d t

inverse oflaplace (s^4+10)/(s-2)inverse laplace

\frac{s ^{4} + 10}{s - 2}

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)