derivative of-3cot(xcsc(x))

Lösung

\frac{d}{d x} (- 3 cot (x) csc (x))

- 3 csc (x) + 6 csc^{3} (x)

Schritte zur Lösung

\frac{d}{d x} (- 3 cot (x) csc (x))

Entferne die Konstante:

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

= - 3 \frac{d}{d x} (cot (x) csc (x))

Wende die Produktregel an:

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

f = cot (x), g = csc (x)

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

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

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

= - 3 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Vereinfache

- 3 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 3 csc (x) + 6 csc^{3} (x)

= - 3 csc (x) + 6 csc^{3} (x)

\frac{d}{d x} ((1 + x^{4} tan (x))^{- 5})

x \to 4 + lim (\frac{3 + x}{4 - x})

d er i v a t i v e f (x) = \frac{3 x ^{5}}{5} - \frac{10 x ^{4}}{3}

\frac{d y}{d x} = \frac{3 x ^{2}}{y}

l a pl a ce t r an s f or m 2 sin^{2} (t)