(\partial)/(\partial x)(e^xtan(x-y))

Lösung

\frac{\partial}{\partial x} (e^{x} tan (x - y))

e^{x} tan (x - y) + sec^{2} (x - y) e^{x}

Schritte zur Lösung

\frac{\partial}{\partial x} (e^{x} tan (x - y))

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{x}, g = tan (x - y)

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

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

\frac{\partial}{\partial x} (tan (x - y)) = sec^{2} (x - y)

= e^{x} tan (x - y) + sec^{2} (x - y) e^{x}