derivative of arctan(x+2y)

Lösung

\frac{d}{d x} (arctan (x + 2 y))

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

Schritte zur Lösung

\frac{d}{d x} (arctan (x + 2 y))

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\int sin (3 x) \cdot sin (5 x) d x

x \to 0 lim (- \frac{2}{x})

\frac{d}{d x} (\frac{1}{5 x - 1})

d er i v a t i v e arcsin (x^{4})

d er i v a t i v e f (x) = \frac{7}{x}