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Beliebt Rechnen >

(\partial)/(\partial y)(-2ye^{x^2-y^2})

Lösung

\frac{\partial}{\partial y} (- 2 y e^{x^{2} - y^{2}})

Lösung

- 2 (e^{x^{2} - y^{2}} - 2 e^{x^{2} - y^{2}} y^{2})

Schritte zur Lösung

\frac{\partial}{\partial y} (- 2 y e^{x^{2} - y^{2}})

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = e^{x^{2} - y^{2}}

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

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

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

= - 2 (1 \cdot e^{x^{2} - y^{2}} + (- 2 e^{x^{2} - y^{2}} y) y)

Vereinfache

- 2 (1 \cdot e^{x^{2} - y^{2}} + (- 2 e^{x^{2} - y^{2}} y) y) : - 2 (e^{x^{2} - y^{2}} - 2 e^{x^{2} - y^{2}} y^{2})

= - 2 (e^{x^{2} - y^{2}} - 2 e^{x^{2} - y^{2}} y^{2})

Beliebte Beispiele

integral of (sqrt(1+(9x)/8))

\int (1 + \frac{9 x}{8}) d x

xy^'+y=-2xy^2,y(1)=-2

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

tangent f(x)=x^3+4x^2+5x,\at x=-1

t an g e n t f (x) = x^{3} + 4 x^{2} + 5 x, at x = - 1

integral of 1/(sqrt(4x^2+12x+16))

\int \frac{1}{4 x ^{2} + 12 x + 16} d x

steigung (7,-5),(-7,-5)

s l o p e (7, - 5), (- 7, - 5)