(\partial)/(\partial x)(6x^3y+6y^5+1)

Lösung

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

18 x^{2} y

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (6 x^{3} y) + \frac{\partial}{\partial x} (6 y^{5}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (6 x^{3} y) = 18 y x^{2}

\frac{\partial}{\partial x} (6 y^{5}) = 0

\frac{\partial}{\partial x} (1) = 0

= 18 y x^{2} + 0 + 0

Vereinfache

= 18 x^{2} y

\int_{1}^{R} x^{- \frac{7}{5}} d x

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

\frac{\partial}{\partial x} (e^{x + y + 5})

\frac{\partial}{\partial z} (\frac{x - y}{x + z})

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{1 + t ^{2}}