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Beliebt Rechnen >

(\partial)/(\partial x)(yx^3-xy^2+xy+13y)

Lösung

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 y)

Lösung

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

Schritte zur Lösung

\frac{\partial}{\partial x} (y x^{3} - x y^{2} + x y + 13 y)

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (y x^{3}) - \frac{\partial}{\partial x} (x y^{2}) + \frac{\partial}{\partial x} (x y) + \frac{\partial}{\partial x} (13 y)

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

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

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

\frac{\partial}{\partial x} (13 y) = 0

= 3 y x^{2} - y^{2} + y + 0

Vereinfache

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

Beliebte Beispiele

integral of x/(x^2+y^2)

\int \frac{x}{x ^{2} + y ^{2}} d y

tangent f(x)=9e^x,\at x=7

t an g e n t f (x) = 9 e^{x}, at x = 7

integral from 1 to 12 of 1/(x-7)

\int_{1}^{12} \frac{1}{x - 7} d x

(\partial)/(\partial y)(sqrt(x^2+6xy+4y^2))

\frac{\partial}{\partial y} (x^{2} + 6 x y + 4 y^{2})

integral of x^2+2x+1

\int x^{2} + 2 x + 1 d x