(\partial)/(\partial x)(4e^{x^2y}xy)

Lösung

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

4 y (2 e^{x^{2} y} x^{2} y + e^{x^{2} y})

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 y \frac{\partial}{\partial x} (e^{x^{2} y} x)

Wende die Produktregel an:

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

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

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

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

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

= 4 y (e^{x^{2} y} \cdot 2 y xx + 1 \cdot e^{x^{2} y})

Vereinfache

4 y (e^{x^{2} y} \cdot 2 y xx + 1 \cdot e^{x^{2} y}) : 4 y (2 e^{x^{2} y} x^{2} y + e^{x^{2} y})

= 4 y (2 e^{x^{2} y} x^{2} y + e^{x^{2} y})

\int \frac{4 x ^{5} + 10 x ^{3}}{x ^{2}} d x

\int \frac{3 x - 5}{x} d x

\frac{d y}{d x} = 0.72 - \frac{9 y}{1000}, y (0) = 80

\int_{- 1}^{1} x (x^{2} + 9)^{3} d x

d er i v a t i v e 3 3 + tan (t)