(\partial)/(\partial x)(x^8+2^y+x^y)

Lösung

\frac{\partial}{\partial x} (x^{8} + 2^{y} + x^{y})

8 x^{7} + y x^{y - 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{8} + 2^{y} + x^{y})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{8}) + \frac{\partial}{\partial x} (2^{y}) + \frac{\partial}{\partial x} (x^{y})

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

\frac{\partial}{\partial x} (2^{y}) = 0

\frac{\partial}{\partial x} (x^{y}) = y x^{y - 1}

= 8 x^{7} + 0 + y x^{y - 1}

Vereinfache

= 8 x^{7} + y x^{y - 1}

y^{^{'}} = \frac{x}{y ^{2}}

t \frac{d y}{d t} + 2 y = t^{2}

\int_{1}^{9} \frac{3 x - 2}{x} d x

\int sec^{3} (5 x) tan^{2} (5 x) d x

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