What is the derivative of (1/2)^x-x ?

The derivative of (1/2)^x-x is -ln(2)(1/2)^x-1

What is the first derivative of (1/2)^x-x ?

The first derivative of (1/2)^x-x is -ln(2)(1/2)^x-1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

(\frac{1}{2})^{x} - x

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

What is the derivative of (1/2)^x-x ?
The derivative of (1/2)^x-x is -ln(2)(1/2)^x-1
What is the first derivative of (1/2)^x-x ?
The first derivative of (1/2)^x-x is -ln(2)(1/2)^x-1