(\partial)/(\partial x)(arcsin(7xyz))

Lösung

\frac{\partial}{\partial x} (arcsin (7 x yz))

\frac{7 yz}{1 - 49 x ^{2} y ^{2} z ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (arcsin (7 x yz))

Behandle

y, z

als Konstanten

Wende die Kettenregel an:

\frac{1}{1 - ( 7 x yz ) ^{2}} \frac{\partial}{\partial x} (7 x yz)

= \frac{1}{1 - ( 7 x yz ) ^{2}} \frac{\partial}{\partial x} (7 x yz)

\frac{\partial}{\partial x} (7 x yz) = 7 yz

= \frac{1}{1 - ( 7 x yz ) ^{2}} \cdot 7 yz

Vereinfache

\frac{1}{1 - ( 7 x yz ) ^{2}} \cdot 7 yz : \frac{7 yz}{1 - 49 x ^{2} y ^{2} z ^{2}}

= \frac{7 yz}{1 - 49 x ^{2} y ^{2} z ^{2}}

x \to - 5 lim (\frac{3}{x - 5})

\frac{\partial}{\partial x} (\frac{( x y )}{( x + y )})

\frac{d}{d x} (9 cos (9 x))

f (x) = cos (x^{l n (x^{2} + 1)})

n = 0 \sum \infty \frac{n !}{3 ^{n}}