(\partial)/(\partial x)(x-3y^2+4x^2y^3)

Lösung

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

8 x y^{3} + 1

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

\frac{\partial}{\partial x} (4 x^{2} y^{3}) = 8 y^{3} x

= 1 - 0 + 8 y^{3} x

Vereinfache

= 8 x y^{3} + 1

y^{^{''}} - 4 y^{^{'}} = 6 t

in v erse l a pl a ce \frac{7 s ^{3} - 9 s + 1}{3 s ^{5}}

\frac{\partial}{\partial z} (cos (x y))

x y y^{^{'}} - y^{2} = x^{4}

d er i v a t i v e e^{x} \cdot ln (x)