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Popular >

derivative of f(x)=arctan(cos(x))

Solution

derivative of

f (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

derivative of 3x^3+5x

\frac{d}{d x} (3 x^{3} + 5 x)

derivative of sqrt(x)(2-x^2)

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

(\partial)/(\partial x)(xe^{-3z+2y})

\frac{\partial}{\partial x} (x e^{- 3 z + 2 y})

derivative of arccos(3x^2)derivative of

arccos (3 x^{2})

derivative of e^{1-cos(x})

\frac{d}{d x} (e^{1 - c o s (x)})

Frequently Asked Questions (FAQ)

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