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

Lösung

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

3 x^{2} + y x^{y - 1}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

\frac{\partial}{\partial x} (x^{3}) = 3 x^{2}

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

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

= 3 x^{2} + 0 + y x^{y - 1}

Vereinfache

= 3 x^{2} + y x^{y - 1}

\int sec (θ) d θ

n = 1 \sum \infty \frac{n !}{2 ^{n}}

\int \frac{1}{( y - 1 ) ( y + 1 )} d y

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{5 x ^{\frac{4}{5}}})

t an g e n t y = e^{4 x} cos (π x), (0, 1)