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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y, z

als Konstanten

Wende die Produktregel an:

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

f = e^{x^{2} y^{4}}, g = sin (x yz)

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

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

\frac{\partial}{\partial x} (sin (x yz)) = cos (x yz) yz

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

d er i v a t i v e 4 (e^{x})^{9}

y^{^{''}} - y^{^{'}} = x

\frac{d}{d x} ((2 x)^{- 4} - (2 t^{- 1})^{2})

d er i v a t i v e (4 x^{2} - 5 x) e^{x}

a re a 7 - x^{2}, x^{2} - 1