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Beliebt Rechnen >

(\partial)/(\partial x)((e^x+e^y)^8)

Lösung

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{8})

Lösung

8 (e^{x} + e^{y})^{7} e^{x}

Schritte zur Lösung

\frac{\partial}{\partial x} ((e^{x} + e^{y})^{8})

Behandle

y

als Konstante

Wende die Kettenregel an:

8 (e^{x} + e^{y})^{7} \frac{\partial}{\partial x} (e^{x} + e^{y})

= 8 (e^{x} + e^{y})^{7} \frac{\partial}{\partial x} (e^{x} + e^{y})

\frac{\partial}{\partial x} (e^{x} + e^{y}) = e^{x}

= 8 (e^{x} + e^{y})^{7} e^{x}

Beliebte Beispiele

integral of (e^u)/((6-e^u)^2)

\int \frac{e ^{u}}{( 6 - e ^{u} ) ^{2}} d u

integral of 4xsec(x)tan(x)

\int 4 x sec (x) tan (x) d x

(\partial)/(\partial x)(x^3y^5+2x^4y)

\frac{\partial}{\partial x} (x^{3} y^{5} + 2 x^{4} y)

derivative-(9x)/y

d er i v a t i v e - \frac{9 x}{y}

integral of (3x-1)^{-4}

\int (3 x - 1)^{- 4} d x