(\partial)/(\partial x)(x^3y^4+x^4y^3)

Lösung

\frac{\partial}{\partial x} (x^{3} y^{4} + x^{4} y^{3})

3 y^{4} x^{2} + 4 y^{3} x^{3}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{3} y^{4} + x^{4} y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{3} y^{4}) + \frac{\partial}{\partial x} (x^{4} y^{3})

\frac{\partial}{\partial x} (x^{3} y^{4}) = 3 y^{4} x^{2}

\frac{\partial}{\partial x} (x^{4} y^{3}) = 4 y^{3} x^{3}

= 3 y^{4} x^{2} + 4 y^{3} x^{3}

\frac{\partial}{\partial x} (e^{\frac{6}{x}})

\frac{d}{d t} (e^{- t} (2 cos (\frac{t}{2}) - 3 sin (\frac{t}{2})))

d er i v a t i v e \frac{7}{4 x ^{5}}

\frac{d x}{d t} = (\frac{6 x}{2000 + 12 t})

\int_{1}^{4} 1 e^{x} d x