(\partial)/(\partial x)(x^2sin(xy+z))

Lösung

\frac{\partial}{\partial x} (x^{2} sin (x y + z))

2 x sin (x y + z) + cos (x y + z) y x^{2}

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} sin (x y + z))

Behandle

y, z

als Konstanten

Wende die Produktregel an:

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

f = x^{2}, g = sin (x y + z)

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

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

\frac{\partial}{\partial x} (sin (x y + z)) = cos (x y + z) y

= 2 x sin (x y + z) + cos (x y + z) y x^{2}

2 x y^{^{'}} - 2 x y = - e^{- 2 x} y^{3}

d er i v a t i v e (x + 2) (x - 5) (x - 1)

x \to 0 lim (3 (h + 2 x) 2)

\int \frac{5}{x + 2} d x

\frac{d}{d x} (4 x^{2} (3 x - 1)^{3})