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Beliebt Rechnen >

derivative of cos(arctan(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Kettenregel an:

- 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}

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of 6e^{2x}

\int 6 e^{2 x} d x

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

d er i v a t i v e 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