derivative of x^2csc(5x)

Lösung

\frac{d}{d x} (x^{2} csc (5 x))

2 x csc (5 x) - 5 x^{2} cot (5 x) csc (5 x)

Schritte zur Lösung

\frac{d}{d x} (x^{2} csc (5 x))

Wende die Produktregel an:

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

f = x^{2}, g = csc (5 x)

= \frac{d}{d x} (x^{2}) csc (5 x) + \frac{d}{d x} (csc (5 x)) x^{2}

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

\frac{d}{d x} (csc (5 x)) = - cot (5 x) csc (5 x) \cdot 5

= 2 x csc (5 x) + (- cot (5 x) csc (5 x) \cdot 5) x^{2}

Vereinfache

= 2 x csc (5 x) - 5 x^{2} cot (5 x) csc (5 x)

\int cot (x) csc^{2} (x) d x

x \to \frac{π}{4} lim (csc (x))

\frac{\partial}{\partial x} (2 x^{y} + 8 y^{x} + 10)

\frac{d ^{2} y}{d x ^{2}} + 14 \frac{d y}{d x} + 49 y = 0

\int 5 sec (x) d x