(\partial)/(\partial z)(tan(3+2x^2y^3z^2))

Lösung

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

sec^{2} (3 + 2 x^{2} y^{3} z^{2}) \cdot 4 x^{2} y^{3} z

Schritte zur Lösung

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

Behandle

x, y

als Konstanten

Wende die Kettenregel an:

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

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

\frac{\partial}{\partial z} (3 + 2 x^{2} y^{3} z^{2}) = 4 x^{2} y^{3} z

= sec^{2} (3 + 2 x^{2} y^{3} z^{2}) \cdot 4 x^{2} y^{3} z

t an g e n t (2 x + 1)^{\frac{1}{5}}, at x = 2

n = 0 \sum \infty \frac{n}{( n ^{2} + 3 )}

\frac{d}{d y} (2 x y)

d er i v a t i v e f (x) = - \frac{12}{s ^{5}}

d er i v a t i v e \frac{4}{3} π \cdot r^{2}