What is the derivative of (6x+5^x) ?

The derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x

What is the first derivative of (6x+5^x) ?

The first derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} ((6 x + 5)^{x})

(ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

Solution steps

\frac{d}{d x} ((6 x + 5)^{x})

Apply exponent rule:

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

(6 x + 5)^{x} = e^{x l n (6 x + 5)}

= \frac{d}{d x} (e^{x l n (6 x + 5)})

Apply the chain rule:

e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

= e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

\frac{d}{d x} (x ln (6 x + 5)) = ln (6 x + 5) + \frac{6 x}{6 x + 5}

= e^{x l n (6 x + 5)} (ln (6 x + 5) + \frac{6 x}{6 x + 5})

e^{x l n (6 x + 5)} = (6 x + 5)^{x}

= (ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

What is the derivative of (6x+5^x) ?
The derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x
What is the first derivative of (6x+5^x) ?
The first derivative of (6x+5^x) is (ln(6x+5)+(6x)/(6x+5))(6x+5)^x