What is the derivative of log_{4}(xe^x) ?

The derivative of log_{4}(xe^x) is 1/(2ln(2)x)+log_{4}(e)

What is the first derivative of log_{4}(xe^x) ?

The first derivative of log_{4}(xe^x) is 1/(2ln(2)x)+log_{4}(e)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (lo g_{4} (x e^{x}))

\frac{1}{2 ln ( 2 ) x} + lo g_{4} (e)

Solution steps

\frac{d}{d x} (lo g_{4} (x e^{x}))

Simplify

lo g_{4} (x e^{x}) : lo g_{4} (x) + lo g_{4} (e) x

= \frac{d}{d x} (lo g_{4} (x) + lo g_{4} (e) x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (lo g_{4} (x)) + \frac{d}{d x} (lo g_{4} (e) x)

\frac{d}{d x} (lo g_{4} (x)) = \frac{1}{2 ln ( 2 ) x}

\frac{d}{d x} (lo g_{4} (e) x) = lo g_{4} (e)

= \frac{1}{2 ln ( 2 ) x} + lo g_{4} (e)

What is the derivative of log_{4}(xe^x) ?
The derivative of log_{4}(xe^x) is 1/(2ln(2)x)+log_{4}(e)
What is the first derivative of log_{4}(xe^x) ?
The first derivative of log_{4}(xe^x) is 1/(2ln(2)x)+log_{4}(e)