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Beliebt Rechnen >

derivative f(x)=ln(16sin^2(x))

Lösung

ableitung von

f (x) = ln (16 sin^{2} (x))

Lösung

2 cot (x)

Schritte zur Lösung

\frac{d}{d x} (ln (16 sin^{2} (x)))

Wende die Kettenregel an:

\frac{1}{16 sin ^{2} ( x )} \frac{d}{d x} (16 sin^{2} (x))

= \frac{1}{16 sin ^{2} ( x )} \frac{d}{d x} (16 sin^{2} (x))

\frac{d}{d x} (16 sin^{2} (x)) = 32 sin (x) cos (x)

= \frac{1}{16 sin ^{2} ( x )} \cdot 32 sin (x) cos (x)

Vereinfache

\frac{1}{16 sin ^{2} ( x )} \cdot 32 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

Graph

Beliebte Beispiele

derivative of (2x^3-x^2+6x+1^3)

\frac{d}{d x} ((2 x^{3} - x^{2} + 6 x + 1)^{3})

derivative sqrt(x^2-9)

d er i v a t i v e x^{2} - 9

integral from 0 to 6 of sqrt(6x+64)

\int_{0}^{6} 6 x + 64 d x

integral of x/((x+1))

\int \frac{x}{( x + 1 )} d x

tangent f(x)= 4/(x+1),\at x=6

t an g e n t f (x) = \frac{4}{x + 1}, at x = 6