derivative of csc((ln(x+3)/(x^2)))

Lösung

\frac{d}{d x} (csc (\frac{ln ( x + 3 )}{x ^{2}}))

- \frac{cot ( \frac{l n ( x + 3 )}{x ^{2}} ) csc ( \frac{l n ( x + 3 )}{x ^{2}} ) ( x - 2 ln ( x + 3 ) ( x + 3 ) )}{x ^{3} ( x + 3 )}

Schritte zur Lösung

\frac{d}{d x} (csc (\frac{ln ( x + 3 )}{x ^{2}}))

Wende die Kettenregel an:

- cot (\frac{ln ( x + 3 )}{x ^{2}}) csc (\frac{ln ( x + 3 )}{x ^{2}}) \frac{d}{d x} (\frac{ln ( x + 3 )}{x ^{2}})

= - cot (\frac{ln ( x + 3 )}{x ^{2}}) csc (\frac{ln ( x + 3 )}{x ^{2}}) \frac{d}{d x} (\frac{ln ( x + 3 )}{x ^{2}})

\frac{d}{d x} (\frac{ln ( x + 3 )}{x ^{2}}) = \frac{x - 2 ln ( x + 3 ) ( x + 3 )}{x ^{3} ( x + 3 )}

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{cot ( \frac{l n ( x + 3 )}{x ^{2}} ) csc ( \frac{l n ( x + 3 )}{x ^{2}} ) ( x - 2 ln ( x + 3 ) ( x + 3 ) )}{x ^{3} ( x + 3 )}

\int e^{y^{2}} y d y

\int \frac{( 3 x ^{2} - x + 2 e )}{x ^{2}} d x

\int \frac{x}{5 - x ^{2}} d x

\frac{d}{d y} (2 y)

x \to 3 - lim (\frac{∣ 3 - x ∣}{3 - x})