What is the derivative of log_{8}(xe^x) ?

The derivative of log_{8}(xe^x) is 1/(3ln(2)x)+log_{8}(e)

What is the first derivative of log_{8}(xe^x) ?

The first derivative of log_{8}(xe^x) is 1/(3ln(2)x)+log_{8}(e)

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derivative of

lo g_{8} (x e^{x})

\frac{1}{3 ln ( 2 ) x} + lo g_{8} (e)

Solution steps

\frac{d}{d x} (lo g_{8} (x e^{x}))

Simplify

lo g_{8} (x e^{x}) : lo g_{8} (x) + lo g_{8} (e) x

= \frac{d}{d x} (lo g_{8} (x) + lo g_{8} (e) x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (lo g_{8} (x)) + \frac{d}{d x} (lo g_{8} (e) x)

\frac{d}{d x} (lo g_{8} (x)) = \frac{1}{3 ln ( 2 ) x}

\frac{d}{d x} (lo g_{8} (e) x) = lo g_{8} (e)

= \frac{1}{3 ln ( 2 ) x} + lo g_{8} (e)

\frac{d}{d x} (- tan (x) - 5 cot (x))

\frac{- 3 sin ( t )}{28}

\int_{1}^{2} e^{1 - x} d x

f (x) = - 3 x^{2}

\int_{0}^{1} x 2 - x^{2} d x

What is the derivative of log_{8}(xe^x) ?
The derivative of log_{8}(xe^x) is 1/(3ln(2)x)+log_{8}(e)
What is the first derivative of log_{8}(xe^x) ?
The first derivative of log_{8}(xe^x) is 1/(3ln(2)x)+log_{8}(e)