derivative of arctan(xsqrt(t))

Lösung

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

\frac{t}{x ^{2} t + 1}

Schritte zur Lösung

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

Behandle

t

als Konstante

Wende die Kettenregel an:

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

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

\frac{d}{d x} (x t) = t

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

Vereinfache

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

= \frac{t}{x ^{2} t + 1}

\frac{\partial}{\partial x} (\frac{3 x}{x ^{2} + 2})

\frac{d}{d x} (8 x^{2} sin (x) tan (x))

\frac{d y}{d x} = \frac{y ^{2} - y}{x}

x^{2} y^{^{''}} - 4 x y^{^{'}} + 6 y = 0, y (1) = 0.4, y^{^{'}} (1) = 0

y^{^{'''}} - 7 y^{^{''}} + 8 y^{^{'}} + 16 y = 0