derivative of log_{5}(xe^x)

Lösung

\frac{d}{d x} (lo g_{5} (x e^{x}))

\frac{1}{x ln ( 5 )} + lo g_{5} (e)

Schritte zur Lösung

\frac{d}{d x} (lo g_{5} (x e^{x}))

Vereinfache

lo g_{5} (x e^{x}) : lo g_{5} (x) + lo g_{5} (e) x

= \frac{d}{d x} (lo g_{5} (x) + lo g_{5} (e) x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (lo g_{5} (x)) + \frac{d}{d x} (lo g_{5} (e) x)

\frac{d}{d x} (lo g_{5} (x)) = \frac{1}{x ln ( 5 )}

\frac{d}{d x} (lo g_{5} (e) x) = lo g_{5} (e)

= \frac{1}{x ln ( 5 )} + lo g_{5} (e)

\int \frac{tan ^{2} ( x )}{4} d x

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y^{^{'}} - \frac{6}{x} y = x^{- 4} y^{5}, y (1) = 1

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