What is the derivative of log_{3}(xe^x) ?

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

What is the first derivative of log_{3}(xe^x) ?

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

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\frac{d}{d x} (lo g_{3} (x e^{x}))

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

Solution steps

\frac{d}{d x} (lo g_{3} (x e^{x}))

Simplify

lo g_{3} (x e^{x}) : lo g_{3} (x) + lo g_{3} (e) x

= \frac{d}{d x} (lo g_{3} (x) + lo g_{3} (e) x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (lo g_{3} (x)) + \frac{d}{d x} (lo g_{3} (e) x)

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

\frac{d}{d x} (lo g_{3} (e) x) = lo g_{3} (e)

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

y = (x^{3} - 4 x)^{8}, (2, 0)

\frac{d}{d t} (\frac{e ^{t b} - e ^{t a}}{t ( b - a )})

y^{^{''}} + 9 y = 12 sin (3 t)

x \to 2 lim (\frac{x ^{3}}{3} - 7 x^{2})

f (y) = y^{4}

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