derivative of 15e^{1/x}

Lösung

\frac{d}{d x} (15 e^{\frac{1}{x}})

- \frac{15 e ^{\frac{1}{x}}}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (15 e^{\frac{1}{x}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 15 \frac{d}{d x} (e^{\frac{1}{x}})

Wende die Kettenregel an:

e^{\frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

= e^{\frac{1}{x}} \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (\frac{1}{x}) = - \frac{1}{x ^{2}}

= 15 e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

Vereinfache

15 e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{15 e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{15 e ^{\frac{1}{x}}}{x ^{2}}

x \to 0 + lim (x ln (tan (9 x)))

d y - (y - 2)^{2} d x = 0

\int_{- 2 π}^{π} cos^{2} (x) d x

x \to \infty lim ((1 + (\frac{2}{x}))^{3 x})

x \to 4 lim (\frac{- 1}{x ^{2} - 16})