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Beliebt Rechnen >

derivative y=ln(x)sec^3(x)

Lösung

ableitung von

y = ln (x) sec^{3} (x)

Lösung

\frac{sec ^{3} ( x )}{x} + 3 sec^{3} (x) tan (x) ln (x)

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = sec^{3} (x)

= \frac{d}{d x} (ln (x)) sec^{3} (x) + \frac{d}{d x} (sec^{3} (x)) ln (x)

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

= \frac{1}{x} sec^{3} (x) + 3 sec^{3} (x) tan (x) ln (x)

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

= \frac{sec ^{3} ( x )}{x} + 3 sec^{3} (x) tan (x) ln (x)

Graph

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