(\partial)/(\partial x)(x^4-5xy+y^4)

Lösung

\frac{\partial}{\partial x} (x^{4} - 5 x y + y^{4})

4 x^{3} - 5 y

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{4} - 5 x y + y^{4})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (5 x y) + \frac{\partial}{\partial x} (y^{4})

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

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

\frac{\partial}{\partial x} (y^{4}) = 0

= 4 x^{3} - 5 y + 0

Vereinfache

= 4 x^{3} - 5 y

d er i v a t i v e f (x) = \frac{x ^{2} + 4 x + 3}{x}

y^{^{'}} tan^{- 1} (x) - y (1 + x^{2})^{- 1} = 0

\frac{d}{d x} (cos (x) + 2 sin (x) cos (x))

\int \frac{w}{1 + w ^{2}} d w

d er i v a t i v e \frac{x}{x ^{2} + 14 x + 45}