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Beliebt Rechnen >

(\partial)/(\partial x)((x+y)e^{y^2})

Lösung

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

Lösung

e^{y^{2}}

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= e^{y^{2}} (1 + 0)

Vereinfache

= e^{y^{2}}

Beliebte Beispiele

integral of (sin(x^2))

\int (sin (x^{2})) d x

(\partial)/(\partial x)(sqrt(9+x^2+y^2))

\frac{\partial}{\partial x} (9 + x^{2} + y^{2})

(d^2)/(dx^2)((10)/(3x^3))

\frac{d ^{2}}{d x ^{2}} (\frac{10}{3 x ^{3}})

(\partial)/(\partial x)(x^2-xy^2+4y^5)

\frac{\partial}{\partial x} (x^{2} - x y^{2} + 4 y^{5})

derivative f(x)=12sqrt(x)

d er i v a t i v e f (x) = 12 x