(\partial)/(\partial y)(3xyz+xy^2-xz^3)

Lösung

\frac{\partial}{\partial y} (3 x yz + x y^{2} - x z^{3})

3 x z + 2 x y

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x yz + x y^{2} - x z^{3})

Behandle

x, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (3 x yz) + \frac{\partial}{\partial y} (x y^{2}) - \frac{\partial}{\partial y} (x z^{3})

\frac{\partial}{\partial y} (3 x yz) = 3 x z

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

\frac{\partial}{\partial y} (x z^{3}) = 0

= 3 x z + 2 x y - 0

Vereinfache

= 3 x z + 2 x y

42 y^{^{''}} + 29 y^{^{'}} - 5 y = 0

n = 1 \sum \infty \frac{n}{( 3 + n )}

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

\frac{d}{d x} (\frac{1 + x ^{2}}{1 + x})

d er i v a t i v e \frac{16}{( 1 - x ) ^{3}}