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Beliebt Rechnen >

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

Lösung

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

Lösung

4 x^{3} y^{3}

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

Beliebte Beispiele

d/(d{y)}(ln({x}+2{y}+3{z}))

\frac{d}{d y} (ln (x + 2 y + 3 z))

limit as x approaches 5-of 2/(x-5)+1

x \to 5 - lim (\frac{2}{x - 5} + 1)

derivative-4x^2+1

d er i v a t i v e - 4 x^{2} + 1

(\partial)/(\partial y)(sin(x^5-7y))

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

(dy)/(dx)=(4/(x^2+1))(y+1)

\frac{d y}{d x} = (\frac{4}{x ^{2} + 1}) (y + 1)