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Beliebt Rechnen >

(\partial)/(\partial y)(e^{7xe^y})

Lösung

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

Lösung

7 e^{7 e^{y} x + y} x

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= e^{7 x e^{y}} \cdot 7 x e^{y}

Wende Exponentenregel an:

a^{b} \cdot a^{c} = a^{b + c}

e^{7 x e^{y}} e^{y} = e^{7 e^{y} x + y}

= 7 e^{7 e^{y} x + y} x

Beliebte Beispiele

derivative f(x)=6x^3cot(x)

d er i v a t i v e f (x) = 6 x^{3} cot (x)

tangent f(x)=x^3sqrt(5-x^2),\at x=2

t an g e n t f (x) = x^{3} 5 - x^{2}, at x = 2

derivative of-1/2 e^{-x^2}

\frac{d}{d x} (- \frac{1}{2} e^{- x^{2}})

(\partial)/(\partial x)(sqrt(x^3+sin(3y)))

\frac{\partial}{\partial x} (x^{3} + sin (3 y))

integral of 1/(sqrt(x^2+c))

\int \frac{1}{x ^{2} + c} d x