derivative f(x)=ln(81sin^2(x))

Lösung

ableitung von

f (x) = ln (81 sin^{2} (x))

2 cot (x)

Schritte zur Lösung

\frac{d}{d x} (ln (81 sin^{2} (x)))

Wende die Kettenregel an:

\frac{1}{81 sin ^{2} ( x )} \frac{d}{d x} (81 sin^{2} (x))

= \frac{1}{81 sin ^{2} ( x )} \frac{d}{d x} (81 sin^{2} (x))

\frac{d}{d x} (81 sin^{2} (x)) = 162 sin (x) cos (x)

= \frac{1}{81 sin ^{2} ( x )} \cdot 162 sin (x) cos (x)

Vereinfache

\frac{1}{81 sin ^{2} ( x )} \cdot 162 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

\frac{d}{d x} (\frac{2 x + 1}{3 x - 2})

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