(\partial)/(\partial y)(tan(y/x))

Lösung

\frac{\partial}{\partial y} (tan (\frac{y}{x}))

\frac{sec ^{2} ( \frac{y}{x} )}{x}

Schritte zur Lösung

\frac{\partial}{\partial y} (tan (\frac{y}{x}))

Behandle

x

als Konstante

Wende die Kettenregel an:

sec^{2} (\frac{y}{x}) \frac{\partial}{\partial y} (\frac{y}{x})

= sec^{2} (\frac{y}{x}) \frac{\partial}{\partial y} (\frac{y}{x})

\frac{\partial}{\partial y} (\frac{y}{x}) = \frac{1}{x}

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

Vereinfache

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

= \frac{sec ^{2} ( \frac{y}{x} )}{x}

f (x) = sin (7 x)

s l o p e \frac{1}{3} \cdot t^{3} - 9 \cdot t + 2

\int x 1 + \frac{1}{4 x} d x

t an g e n t 3 x + 25, at x = - 3

\int (2 x - 1) ln (5 x) d x