What is the derivative of 11e^{1/x} ?

The derivative of 11e^{1/x} is -(11e^{1/x})/(x^2)

What is the first derivative of 11e^{1/x} ?

The first derivative of 11e^{1/x} is -(11e^{1/x})/(x^2)

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\frac{d}{d x} (11 e^{\frac{1}{x}})

- \frac{11 e ^{\frac{1}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (11 e^{\frac{1}{x}})

Take the constant out:

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

= 11 \frac{d}{d x} (e^{\frac{1}{x}})

Apply the chain rule:

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}}

= 11 e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

Simplify

11 e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{11 e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{11 e ^{\frac{1}{x}}}{x ^{2}}

What is the derivative of 11e^{1/x} ?
The derivative of 11e^{1/x} is -(11e^{1/x})/(x^2)
What is the first derivative of 11e^{1/x} ?
The first derivative of 11e^{1/x} is -(11e^{1/x})/(x^2)