implicit (dy)/(dx),y=(9+x)^{1/x}

Lösung

implizite ableitung

\frac{d y}{d x}, y = (9 + x)^{\frac{1}{x}}

\frac{d y}{d x} = (- \frac{ln ( 9 + x )}{x ^{2}} + \frac{1}{x ( 9 + x )}) (9 + x)^{\frac{1}{x}}

Schritte zur Lösung

y = (9 + x)^{\frac{1}{x}}

Behandle

y

wie

y (x)

Beide Seiten differenzieren:

\frac{d y}{d x} = (- \frac{ln ( 9 + x )}{x ^{2}} + \frac{1}{x ( 9 + x )}) (9 + x)^{\frac{1}{x}}

Isoliere

\frac{d y}{d x} : \frac{d y}{d x} = (- \frac{ln ( 9 + x )}{x ^{2}} + \frac{1}{x ( 9 + x )}) (9 + x)^{\frac{1}{x}}

\frac{d y}{d x} = (- \frac{ln ( 9 + x )}{x ^{2}} + \frac{1}{x ( 9 + x )}) (9 + x)^{\frac{1}{x}}

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