derivative f(x)=5csc^4(x)

Lösung

ableitung von

f (x) = 5 csc^{4} (x)

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

Schritte zur Lösung

\frac{d}{d x} (5 csc^{4} (x))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (csc^{4} (x))

Wende die Kettenregel an:

4 (csc (x))^{3} \frac{d}{d x} (csc (x))

= 4 (csc (x))^{3} \frac{d}{d x} (csc (x))

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

= 5 \cdot 4 (csc (x))^{3} (- cot (x) csc (x))

Vereinfache

5 \cdot 4 csc^{3} (x) (- cot (x) csc (x)) : - 20 csc^{4} (x) cot (x)

= - 20 csc^{4} (x) cot (x)

in v erse l a pl a ce 1 - e^{- s}

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

\int \frac{1}{1 + 3 x} d x

x \to 1 lim (\frac{7}{x ^{3} - 1})

x \to 0 lim (\frac{1}{x} - \frac{1}{x ^{2} - x})