derivative y=sqrt(1+cot^2(x))

Lösung

ableitung von

y = 1 + cot^{2} (x)

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

Schritte zur Lösung

\frac{d}{d x} (1 + cot^{2} (x))

Wende die Kettenregel an:

\frac{1}{2 1 + cot ^{2} ( x )} \frac{d}{d x} (1 + cot^{2} (x))

= \frac{1}{2 1 + cot ^{2} ( x )} \frac{d}{d x} (1 + cot^{2} (x))

\frac{d}{d x} (1 + cot^{2} (x)) = - 2 csc^{2} (x) cot (x)

= \frac{1}{2 1 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x))

Vereinfache

\frac{1}{2 1 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x)) : - \frac{csc ^{2} ( x ) cot ( x )}{csc ^{2} ( x )}

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

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

y^{^{'}} - 5 y = 10

\frac{d}{d x} (x^{9} ln (x))

\frac{d y}{d x} = - \frac{3 x}{y}

\frac{d}{d x} (e^{a t} sin (b t))