derivative of 4xcsc(x)

Lösung

\frac{d}{d x} (4 x csc (x))

4 (csc (x) - x cot (x) csc (x))

Schritte zur Lösung

\frac{d}{d x} (4 x csc (x))

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x csc (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = csc (x)

= 4 (\frac{d x}{d x} csc (x) + \frac{d}{d x} (csc (x)) x)

\frac{d x}{d x} = 1

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

= 4 (1 \cdot csc (x) + (- cot (x) csc (x)) x)

Vereinfache

= 4 (csc (x) - x cot (x) csc (x))

\frac{d}{d x} (\frac{- e ^{x} sin ( x )}{cos ( x )})

in v erse l a pl a ce \frac{s + 2}{( s + 3 ) ( s + 4 )}

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

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

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