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

The derivative of (6x)^{5x} is 5ln(6)*7776^xx^{5x}+5x^{5x}(ln(x)+1)*7776^x

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

The first derivative of (6x)^{5x} is 5ln(6)*7776^xx^{5x}+5x^{5x}(ln(x)+1)*7776^x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

(6 x)^{5 x}

5 ln (6) \cdot 777 6^{x} x^{5 x} + 5 x^{5 x} (ln (x) + 1) \cdot 777 6^{x}

Solution steps

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

Simplify

(6 x)^{5 x} : 777 6^{x} x^{5 x}

= \frac{d}{d x} (777 6^{x} x^{5 x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 777 6^{x}, g = x^{5 x}

= \frac{d}{d x} (777 6^{x}) x^{5 x} + \frac{d}{d x} (x^{5 x}) 777 6^{x}

\frac{d}{d x} (777 6^{x}) = 5 ln (6) \cdot 777 6^{x}

\frac{d}{d x} (x^{5 x}) = 5 x^{5 x} (ln (x) + 1)

= 5 ln (6) \cdot 777 6^{x} x^{5 x} + 5 x^{5 x} (ln (x) + 1) \cdot 777 6^{x}

What is the derivative of (6x)^{5x} ?
The derivative of (6x)^{5x} is 5ln(6)*7776^xx^{5x}+5x^{5x}(ln(x)+1)*7776^x
What is the first derivative of (6x)^{5x} ?
The first derivative of (6x)^{5x} is 5ln(6)*7776^xx^{5x}+5x^{5x}(ln(x)+1)*7776^x