What is the derivative of 5^{-2x} ?

The derivative of 5^{-2x} is -2ln(5)*25^{-x}

What is the first derivative of 5^{-2x} ?

The first derivative of 5^{-2x} is -2ln(5)*25^{-x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (5^{- 2 x})

- 2 ln (5) \cdot 2 5^{- x}

Solution steps

\frac{d}{d x} (5^{- 2 x})

Simplify

5^{- 2 x} : 2 5^{- x}

= \frac{d}{d x} (2 5^{- x})

Apply exponent rule:

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

2 5^{- x} = e^{(- x) l n (25)}

= \frac{d}{d x} (e^{(- x) l n (25)})

Apply the chain rule:

e^{(- x) l n (25)} \frac{d}{d x} ((- x) ln (25))

= e^{(- x) l n (25)} \frac{d}{d x} ((- x) ln (25))

\frac{d}{d x} ((- x) ln (25)) = - 2 ln (5)

= e^{(- x) l n (25)} (- 2 ln (5))

Simplify

e^{(- x) l n (25)} (- 2 ln (5)) : - 2 ln (5) \cdot 2 5^{- x}

= - 2 ln (5) \cdot 2 5^{- x}

What is the derivative of 5^{-2x} ?
The derivative of 5^{-2x} is -2ln(5)*25^{-x}
What is the first derivative of 5^{-2x} ?
The first derivative of 5^{-2x} is -2ln(5)*25^{-x}