derivative of sin(x/y)

Lösung

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

\frac{cos ( \frac{x}{y} ) ( y - x \frac{d y}{d x} )}{y ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= cos (\frac{x}{y}) \frac{y - x \frac{d y}{d x}}{y ^{2}}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ( \frac{x}{y} ) ( y - x \frac{d y}{d x} )}{y ^{2}}

\frac{d}{d x} (\frac{17}{x})

\int \frac{sec ^{2} ( x )}{sec ( x )} d x

\frac{d}{d x} (e^{y x})

t an g e n t f (x) = \frac{3}{x}, (9, \frac{1}{3})

\int (8 x^{3} (2 x^{4} + 4)^{4}) d x