derivative of 2csc^2(x)

Lösung

\frac{d}{d x} (2 csc^{2} (x))

- 4 csc^{2} (x) cot (x)

Schritte zur Lösung

\frac{d}{d x} (2 csc^{2} (x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (csc^{2} (x))

Wende die Kettenregel an:

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

= 2 csc (x) \frac{d}{d x} (csc (x))

\frac{d}{d x} (csc (x)) = - cot (x) csc (x)

= 2 \cdot 2 csc (x) (- cot (x) csc (x))

Vereinfache

2 \cdot 2 csc (x) (- cot (x) csc (x)) : - 4 csc^{2} (x) cot (x)

= - 4 csc^{2} (x) cot (x)

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

\int \frac{4}{x} + \frac{x}{x ^{2} + 5} d x

t an g e n t y = 3 - 9 x^{2}

im pl i c i t \frac{d y}{d x}, e^{x} y = 8

y^{^{'}} = \frac{( x ^{2} y + y ^{3} )}{x ^{3}}