(\partial)/(\partial x)(x^3+y^5+x^7-y^2)

Lösung

\frac{\partial}{\partial x} (x^{3} + y^{5} + x^{7} - y^{2})

7 x^{6} + 3 x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} + y^{5} + x^{7} - y^{2})

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} (y^{5}) + \frac{\partial}{\partial x} (x^{7}) - \frac{\partial}{\partial x} (y^{2})

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

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

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

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

= 3 x^{2} + 0 + 7 x^{6} - 0

Vereinfache

= 7 x^{6} + 3 x^{2}

\frac{\partial}{\partial x} (A x)

\frac{d}{d x} (\frac{e ^{- x} cos ^{2} ( x )}{x ^{2} + x + 1})

\frac{\partial}{\partial x} (\frac{v}{x})

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

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