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Popular >

derivative of cos(arctan(x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

- sin (arctan (x)) \frac{d}{d x} (arctan (x))

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

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

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

Simplify

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

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

Popular Examples

integral of 6e^{2x}

\int 6 e^{2 x} d x

derivative of 4cos(t)-9sin(t)derivative of

4 cos (t) - 9 sin (t)

(\partial)/(\partial x)(x^9yz^2+5yz)

\frac{\partial}{\partial x} (x^{9} y z^{2} + 5 yz)

integral of cos^3(2x)sin^3(2x)

\int cos^{3} (2 x) sin^{3} (2 x) d x

cos(y)y^'=e^{2x}+1

cos (y) y^{^{'}} = e^{2 x} + 1

Frequently Asked Questions (FAQ)

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