(\partial)/(\partial y)(6y^2e^{6xy})

Lösung

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

6 (2 y e^{6 x y} + e^{6 x y} \cdot 6 x y^{2})

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

= 6 \frac{\partial}{\partial y} (y^{2} e^{6 x y})

Wende die Produktregel an:

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

f = y^{2}, g = e^{6 x y}

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

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

\frac{\partial}{\partial y} (e^{6 x y}) = e^{6 x y} \cdot 6 x

= 6 (2 y e^{6 x y} + e^{6 x y} \cdot 6 x y^{2})

\frac{d}{d x} (x^{4} - 12 x^{3} + 48 x^{2} - 64 x)

\int \frac{x - 1}{( 2 x + 5 ) ( x - 8 )} d x

\int \frac{1}{t ^{2} 289 - t ^{2}} d t

\int_{- 7}^{7} \frac{1}{2} (49 - x^{2}) d x

t \to π lim (sin (\frac{t}{2}))