en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 15e^{1/x}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 15 \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}}

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

Simplify

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}}

Popular Examples

limit as x approaches 0+of xln(tan(9x))

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

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

integral from-2pi to pi of cos^2(x)

\int_{- 2 π}^{π} cos^{2} (x) d x

limit as x approaches infinity of (1+(2/x))^{3x}

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

limit as x approaches 4 of (-1)/(x^2-16)

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

Frequently Asked Questions (FAQ)

What is the derivative of 15e^{1/x} ?
The derivative of 15e^{1/x} is -(15e^{1/x})/(x^2)
What is the first derivative of 15e^{1/x} ?
The first derivative of 15e^{1/x} is -(15e^{1/x})/(x^2)