(\partial)/(\partial x)(x^7+3^y+x^y)

Lösung

\frac{\partial}{\partial x} (x^{7} + 3^{y} + x^{y})

7 x^{6} + y x^{y - 1}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{7} + 3^{y} + x^{y})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{7}) + \frac{\partial}{\partial x} (3^{y}) + \frac{\partial}{\partial x} (x^{y})

\frac{\partial}{\partial x} (x^{7}) = 7 x^{6}

\frac{\partial}{\partial x} (3^{y}) = 0

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

= 7 x^{6} + 0 + y x^{y - 1}

Vereinfache

= 7 x^{6} + y x^{y - 1}

\frac{d}{d y} (- ln (y))

y^{^{''}} - 6 y^{^{'}} + 9 y = x e^{x}

s l o p e (- 5, 6), (- 3, 4)

\int \frac{x ^{2}}{( 121 + x ^{2} ) ^{2}} d x

\int \frac{y ^{3} e ^{y^{2}}}{( y ^{2} + 1 ) ^{2}} d y