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

Lösung

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

56 e^{x^{8} y} x^{7} y

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

= 7 e^{x^{8} y} \cdot 8 y x^{7}

Vereinfache

= 56 e^{x^{8} y} x^{7} y

d er i v a t i v e x^{2} (x^{3} + 5)^{3}

\int 7 cos^{2} (x t a) n^{3} x d x

n = 0 \sum \infty \frac{1}{4 n}

\frac{d y}{d x} = y + 8

\int \frac{5 x}{( 6 - x ^{2} ) ^{3}} d x