What is the derivative of ln(xe^{7x}) ?

The derivative of ln(xe^{7x}) is 1/x+7

What is the first derivative of ln(xe^{7x}) ?

The first derivative of ln(xe^{7x}) is 1/x+7

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derivative of

ln (x e^{7 x})

\frac{1}{x} + 7

Solution steps

\frac{d}{d x} (ln (x e^{7 x}))

Simplify

ln (x e^{7 x}) : ln (x) + 7 x

= \frac{d}{d x} (ln (x) + 7 x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (x)) + \frac{d}{d x} (7 x)

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (7 x) = 7

= \frac{1}{x} + 7

d er i v a t i v e f (x) = \frac{32}{x}

\frac{\partial}{\partial x} (4 π^{2} \frac{x}{y ^{2}})

\int \frac{1}{1 - 25 x ^{2}} d x

\frac{d}{d x} (\frac{- 5}{4 x ^{3}})

in v erse l a pl a ce \frac{5 s + 5}{s ( s ^{2} + 6 s + 10 )}

What is the derivative of ln(xe^{7x}) ?
The derivative of ln(xe^{7x}) is 1/x+7
What is the first derivative of ln(xe^{7x}) ?
The first derivative of ln(xe^{7x}) is 1/x+7