(\partial)/(\partial x)(x^2tan(xy))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = x^{2}, g = tan (x y)

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

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

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

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

\frac{d y}{d t} = y + t

\frac{d}{d y} (2 y^{2} + 3 x)

\frac{\partial}{\partial x} (\frac{53}{5 + x ^{2} + y ^{2}})

x \to 1 lim (sin (2 x))

\frac{d}{d x} (5 sin (π x))