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Popular >

derivative of 3e^{1/x}

Solution

derivative of

3 e^{\frac{1}{x}}

Solution

- \frac{3 e ^{\frac{1}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (3 e^{\frac{1}{x}})

Take the constant out:

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

= 3 \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}}

= 3 e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

Simplify

3 e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{3 e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{3 e ^{\frac{1}{x}}}{x ^{2}}

Popular Examples

integral from 0 to pi of sin^2(8x)

\int_{0}^{π} sin^{2} (8 x) d x

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\int_{- 4}^{4} (3 - x) d x

limit as x approaches 0 of (sin(x^2)+1)^{1/(5x^2)}

x \to 0 lim ((sin (x^{2}) + 1)^{\frac{1}{5 x ^{2}}})

derivative of 0.882x^{0.842}

\frac{d}{d x} (0.882 x^{0.842})

limit as x approaches-1-of (3+x)/(x^2-1)

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

Frequently Asked Questions (FAQ)

What is the derivative of 3e^{1/x} ?
The derivative of 3e^{1/x} is -(3e^{1/x})/(x^2)
What is the first derivative of 3e^{1/x} ?
The first derivative of 3e^{1/x} is -(3e^{1/x})/(x^2)