What is the derivative of 2^{-x} ?

The derivative of 2^{-x} is -ln(2)*2^{-x}

What is the first derivative of 2^{-x} ?

The first derivative of 2^{-x} is -ln(2)*2^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

2^{- x}

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{- x} = e^{(- x) l n (2)}

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

Apply the chain rule:

e^{(- x) l n (2)} \frac{d}{d x} ((- x) ln (2))

= e^{(- x) l n (2)} \frac{d}{d x} ((- x) ln (2))

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

= e^{(- x) l n (2)} (- ln (2))

Simplify

e^{(- x) l n (2)} (- ln (2)) : - ln (2) \cdot 2^{- x}

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

x \to 400 - lim (x)

\int \frac{x ^{5}}{4 + x ^{2}} d x

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

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

\int e^{0.05 x} d x

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