(\partial)/(\partial y)(x^5-7x^3y^3+y^6)

Lösung

\frac{\partial}{\partial y} (x^{5} - 7 x^{3} y^{3} + y^{6})

6 y^{5} - 21 x^{3} y^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (x^{5} - 7 x^{3} y^{3} + y^{6})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (x^{5}) - \frac{\partial}{\partial y} (7 x^{3} y^{3}) + \frac{\partial}{\partial y} (y^{6})

\frac{\partial}{\partial y} (x^{5}) = 0

\frac{\partial}{\partial y} (7 x^{3} y^{3}) = 21 x^{3} y^{2}

\frac{\partial}{\partial y} (y^{6}) = 6 y^{5}

= 0 - 21 x^{3} y^{2} + 6 y^{5}

Vereinfache

= 6 y^{5} - 21 x^{3} y^{2}

\int \frac{2 x + 1}{x ^{2} - 7 x + 12} d x

d er i v a t i v e y = e^{4 x}

l o n g d i v i s i o n \frac{x ^{2} - x - 2}{x ^{2} - 6 x + 9}

\int_{1}^{2} f (x) d x

\int \frac{1}{64 x ^{2} - 81} d x