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Beliebt Rechnen >

derivative ln(tan(x^3))

Lösung

ableitung von

ln (tan (x^{3}))

Lösung

3 x^{2} sec^{2} (x^{3}) cot (x^{3})

Schritte zur Lösung

\frac{d}{d x} (ln (tan (x^{3})))

Wende die Kettenregel an:

\frac{1}{tan ( x ^{3} )} \frac{d}{d x} (tan (x^{3}))

= \frac{1}{tan ( x ^{3} )} \frac{d}{d x} (tan (x^{3}))

\frac{d}{d x} (tan (x^{3})) = sec^{2} (x^{3}) \cdot 3 x^{2}

= \frac{1}{tan ( x ^{3} )} sec^{2} (x^{3}) \cdot 3 x^{2}

Vereinfache

\frac{1}{tan ( x ^{3} )} sec^{2} (x^{3}) \cdot 3 x^{2} : 3 x^{2} sec^{2} (x^{3}) cot (x^{3})

= 3 x^{2} sec^{2} (x^{3}) cot (x^{3})

Graph

Beliebte Beispiele

\frac{d x}{d t} = - \frac{t}{x}

laplacetransform e^{2t}sin(4t)

l a pl a ce t r an s f or m e^{2 t} sin (4 t)

derivative (x^3-2)^2

d er i v a t i v e (x^{3} - 2)^{2}

derivative of sqrt(x)-6x

\frac{d}{d x} (x - 6 x)

limit as x approaches 1 of x^3

x \to 1 lim (x^{3})