(\partial)/(\partial x)(1/(sin(x^2-y^2)))

Lösung

\frac{\partial}{\partial x} (\frac{1}{sin ( x ^{2} - y ^{2} )})

- cot (x^{2} - y^{2}) csc (x^{2} - y^{2}) \cdot 2 x

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{1}{sin ( x ^{2} - y ^{2} )})

Vereinfache

\frac{1}{sin ( x ^{2} - y ^{2} )} : csc (x^{2} - y^{2})

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

Behandle

y

als Konstante

Wende die Kettenregel an:

- cot (x^{2} - y^{2}) csc (x^{2} - y^{2}) \frac{\partial}{\partial x} (x^{2} - y^{2})

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

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

= - cot (x^{2} - y^{2}) csc (x^{2} - y^{2}) \cdot 2 x

y^{^{''}} + a = 0

f^{^{'}} (x) = x^{4}

s

\frac{\partial}{\partial y} (x e^{6 y})

\frac{d}{d x} (\frac{2 ^{3 x}}{ln ( 3 )})