derivative f(x)=log_{7}(xe^x)

Lösung

ableitung von

f (x) = lo g_{7} (x e^{x})

\frac{1}{x ln ( 7 )} + lo g_{7} (e)

Schritte zur Lösung

\frac{d}{d x} (lo g_{7} (x e^{x}))

Vereinfache

lo g_{7} (x e^{x}) : lo g_{7} (x) + lo g_{7} (e) x

= \frac{d}{d x} (lo g_{7} (x) + lo g_{7} (e) x)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (lo g_{7} (x)) + \frac{d}{d x} (lo g_{7} (e) x)

\frac{d}{d x} (lo g_{7} (x)) = \frac{1}{x ln ( 7 )}

\frac{d}{d x} (lo g_{7} (e) x) = lo g_{7} (e)

= \frac{1}{x ln ( 7 )} + lo g_{7} (e)

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