en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (2^x/x)

Solution

\frac{d}{d x} (\frac{2 ^{x}}{x})

Solution

\frac{ln ( 2 ) \cdot 2 ^{x} x - 2 ^{x}}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 ^{x}}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (2^{x}) = 2^{x} ln (2)

\frac{d x}{d x} = 1

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

Simplify

= \frac{ln ( 2 ) \cdot 2 ^{x} x - 2 ^{x}}{x ^{2}}

Graph

Popular Examples

limit as x approaches 0 of ((5^x-7^x))/x

x \to 0 lim (\frac{( 5 ^{x} - 7 ^{x} )}{x})

derivative of (-2x^3+x^2-2x-1x^3)

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

(\partial)/(\partial v)({u}(v)(v)^2e^v)

\frac{\partial}{\partial v} (u (v) (v)^{2} e^{v})

derivative of (dy/(dx))=0

\frac{d}{d x} (\frac{d y}{d x}) = 0

derivative of (6x^2+8x+2)/(sqrt(x))derivative of

\frac{6 x ^{2} + 8 x + 2}{x}

Frequently Asked Questions (FAQ)

What is the derivative of (2^x/x) ?
The derivative of (2^x/x) is (ln(2)*2^xx-2^x)/(x^2)
What is the first derivative of (2^x/x) ?
The first derivative of (2^x/x) is (ln(2)*2^xx-2^x)/(x^2)