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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{2}, g = e^{4 x y}

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

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

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

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

\frac{d}{d x} ((x \cdot sinh (x) + cos (x))^{5})

\frac{d}{d x} (\frac{x + 6}{x ^{3} + x - 8})

d er i v a t i v e x^{2} - 2 x - 1

in v erse l a pl a ce \frac{( s + 4 )}{s ^{2} + 4 s + 29}

\int 1