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Beliebt Rechnen >

derivative f(x)=ln(4sin^2(x))

Lösung

ableitung von

f (x) = ln (4 sin^{2} (x))

Lösung

2 cot (x)

Schritte zur Lösung

\frac{d}{d x} (ln (4 sin^{2} (x)))

Wende die Kettenregel an:

\frac{1}{4 sin ^{2} ( x )} \frac{d}{d x} (4 sin^{2} (x))

= \frac{1}{4 sin ^{2} ( x )} \frac{d}{d x} (4 sin^{2} (x))

\frac{d}{d x} (4 sin^{2} (x)) = 4 sin (2 x)

= \frac{1}{4 sin ^{2} ( x )} \cdot 4 sin (2 x)

Vereinfache

\frac{1}{4 sin ^{2} ( x )} \cdot 4 sin (2 x) : 2 cot (x)

= 2 cot (x)

Graph

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