(\partial}{\partial y}(sin(\frac{5x)/y))

Lösung

\frac{\partial}{\partial y} (sin (\frac{5 x}{y}))

- \frac{5 x cos ( \frac{5 x}{y} )}{y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial y} (sin (\frac{5 x}{y}))

Behandle

x

als Konstante

Wende die Kettenregel an:

cos (\frac{5 x}{y}) \frac{\partial}{\partial y} (\frac{5 x}{y})

= cos (\frac{5 x}{y}) \frac{\partial}{\partial y} (\frac{5 x}{y})

\frac{\partial}{\partial y} (\frac{5 x}{y}) = - \frac{5 x}{y ^{2}}

= cos (\frac{5 x}{y}) (- \frac{5 x}{y ^{2}})

Vereinfache

cos (\frac{5 x}{y}) (- \frac{5 x}{y ^{2}}) : - \frac{5 x cos ( \frac{5 x}{y} )}{y ^{2}}

= - \frac{5 x cos ( \frac{5 x}{y} )}{y ^{2}}

a re a y = \frac{4}{x}, y = x, y = 4

\int 5 x^{2} (x^{3} + 1)^{10} d x

d er i v a t i v e f (x) = (5 x^{3} + 4) (3 x^{7} - 5)

\int \frac{x + 4}{x ^{2} + 7 x - 8} d x

2 y^{^{''}} - 3 y^{^{'}} + y = e^{- 3 x}