en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 39e^{1/x}

Solution

\frac{d}{d x} (39 e^{\frac{1}{x}})

Solution

- \frac{39 e ^{\frac{1}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (39 e^{\frac{1}{x}})

Take the constant out:

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

= 39 \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}}

= 39 e^{\frac{1}{x}} (- \frac{1}{x ^{2}})

Simplify

39 e^{\frac{1}{x}} (- \frac{1}{x ^{2}}) : - \frac{39 e ^{\frac{1}{x}}}{x ^{2}}

= - \frac{39 e ^{\frac{1}{x}}}{x ^{2}}

Popular Examples

derivative of e^x(2x^2+x-8)

\frac{d}{d x} (e^{x} (2 x^{2} + x - 8))

integral of-4x^4+8x^3

\int - 4 x^{4} + 8 x^{3} d x

integral of (2x-3)/(x^2+2x-17)

\int \frac{2 x - 3}{x ^{2} + 2 x - 17} d x

y^{1/2}(dy)/(dx)+y^{3/2}=1,y(0)=16

y^{\frac{1}{2}} \frac{d y}{d x} + y^{\frac{3}{2}} = 1, y (0) = 16

integral of (sin(2θ))/(1+sin^2(θ))

\int \frac{sin ( 2 θ )}{1 + sin ^{2} ( θ )} d θ

Frequently Asked Questions (FAQ)

What is the derivative of 39e^{1/x} ?
The derivative of 39e^{1/x} is -(39e^{1/x})/(x^2)
What is the first derivative of 39e^{1/x} ?
The first derivative of 39e^{1/x} is -(39e^{1/x})/(x^2)