What is the derivative of y=5^{9x-5} ?

The derivative of y=5^{9x-5} is 9ln(5)*5^{9x-5}

What is the first derivative of y=5^{9x-5} ?

The first derivative of y=5^{9x-5} is 9ln(5)*5^{9x-5}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

y = 5^{9 x - 5}

9 ln (5) \cdot 5^{9 x - 5}

Solution steps

\frac{d}{d x} (5^{9 x - 5})

Apply exponent rule:

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

5^{9 x - 5} = e^{(9 x - 5) l n (5)}

= \frac{d}{d x} (e^{(9 x - 5) l n (5)})

Apply the chain rule:

e^{(9 x - 5) l n (5)} \frac{d}{d x} ((9 x - 5) ln (5))

= e^{(9 x - 5) l n (5)} \frac{d}{d x} ((9 x - 5) ln (5))

\frac{d}{d x} ((9 x - 5) ln (5)) = 9 ln (5)

= e^{(9 x - 5) l n (5)} \cdot 9 ln (5)

e^{(9 x - 5) l n (5)} = 5^{9 x - 5}

= 9 ln (5) \cdot 5^{9 x - 5}

What is the derivative of y=5^{9x-5} ?
The derivative of y=5^{9x-5} is 9ln(5)*5^{9x-5}
What is the first derivative of y=5^{9x-5} ?
The first derivative of y=5^{9x-5} is 9ln(5)*5^{9x-5}