derivative of csc(\sqrt[3]{sin(2+x^2}))

Lösung

\frac{d}{d x} (csc (3 sin (2 + x^{2})))

- \frac{2 x cos ( 2 + x ^{2} ) cot ( 3 sin ( 2 + x ^{2} ) ) csc ( 3 sin ( 2 + x ^{2} ) )}{3 sin ^{\frac{2}{3}} ( 2 + x ^{2} )}

Schritte zur Lösung

\frac{d}{d x} (csc (3 sin (2 + x^{2})))

Wende die Kettenregel an:

- cot (3 sin (2 + x^{2})) csc (3 sin (2 + x^{2})) \frac{d}{d x} (3 sin (2 + x^{2}))

= - cot (3 sin (2 + x^{2})) csc (3 sin (2 + x^{2})) \frac{d}{d x} (3 sin (2 + x^{2}))

\frac{d}{d x} (3 sin (2 + x^{2})) = \frac{2 x cos ( 2 + x ^{2} )}{3 sin ^{\frac{2}{3}} ( 2 + x ^{2} )}

= - cot (3 sin (2 + x^{2})) csc (3 sin (2 + x^{2})) \frac{2 x cos ( 2 + x ^{2} )}{3 sin ^{\frac{2}{3}} ( 2 + x ^{2} )}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{2 x cos ( 2 + x ^{2} ) cot ( 3 sin ( 2 + x ^{2} ) ) csc ( 3 sin ( 2 + x ^{2} ) )}{3 sin ^{\frac{2}{3}} ( 2 + x ^{2} )}

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

\int (2 - x)^{3} d x

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

\frac{d}{d x} ((sin (x))^{3 x})

\int sin^{5} (4 x) d x