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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{25 cos ( \frac{5 x}{y} )}{y}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

5 cos (\frac{5 x}{y}) \frac{5}{y} : \frac{25 cos ( \frac{5 x}{y} )}{y}

= \frac{25 cos ( \frac{5 x}{y} )}{y}

Beliebte Beispiele

tangent 2x^2+8x

t an g e n t 2 x^{2} + 8 x

derivative of ((x-1(2x+3)+7)^5)

\frac{d}{d x} (((x - 1) (2 x + 3) + 7)^{5})

derivative of ax^2e^{-2x}

\frac{d}{d x} (a x^{2} e^{- 2 x})

integral of (3^x)/(4^x)

\int \frac{3 ^{x}}{4 ^{x}} d x

laplacetransform 1/2 e^{-4t}-1/2 e^{-6t}

l a pl a ce t r an s f or m \frac{1}{2} e^{- 4 t} - \frac{1}{2} e^{- 6 t}