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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{(x + 2) l n (5)})

Apply the chain rule:

e^{(x + 2) l n (5)} \frac{d}{d x} ((x + 2) ln (5))

= e^{(x + 2) l n (5)} \frac{d}{d x} ((x + 2) ln (5))

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

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

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

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

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