derivative of arctan(xy)

Lösung

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

\frac{y + x \frac{d y}{d x}}{x ^{2} y ^{2} + 1}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

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

Vereinfache

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

= \frac{y + x \frac{d y}{d x}}{x ^{2} y ^{2} + 1}

\int \frac{( 3 x - 2 )}{5 x ^{2} - 3 x + 2} d x

d er i v a t i v e f (x) = \frac{3}{1 + x ^{2}}

\int_{0}^{1} 3 x^{2} (x^{3} + 5)^{- 2} d x

\int sin (5 π) t d t

2 y^{^{''}} - 8 y = 0