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Beliebt Rechnen >

(\partial)/(\partial y)(sin(x)+x^2e^y-1)

Lösung

\frac{\partial}{\partial y} (sin (x) + x^{2} e^{y} - 1)

Lösung

e^{y} x^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (sin (x) + x^{2} e^{y} - 1)

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (sin (x)) + \frac{\partial}{\partial y} (x^{2} e^{y}) - \frac{\partial}{\partial y} (1)

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

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

\frac{\partial}{\partial y} (1) = 0

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

Vereinfache

= e^{y} x^{2}

Beliebte Beispiele

derivative of (6x/(5-cot(x)))

\frac{d}{d x} (\frac{6 x}{5 - cot ( x )})

integral of 1/(2+sin(x)+3cos(x))

\int \frac{1}{2 + sin ( x ) + 3 cos ( x )} d x

derivative of sqrt(2x^2+2y^2)

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

integral from-2 to 4 of 10+4x-3x^3

\int_{- 2}^{4} 10 + 4 x - 3 x^{3} d x

integral of x-x/(x^2+1)

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