What is the derivative of f(x)=ln(x^6e^x) ?

The derivative of f(x)=ln(x^6e^x) is 6/x+1

What is the first derivative of f(x)=ln(x^6e^x) ?

The first derivative of f(x)=ln(x^6e^x) is 6/x+1

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derivative of

f (x) = ln (x^{6} e^{x})

\frac{6}{x} + 1

Solution steps

\frac{d}{d x} (ln (x^{6} e^{x}))

Simplify

ln (x^{6} e^{x}) : ln (x^{6}) + x

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d x}{d x} = 1

= \frac{6}{x} + 1

\int 24 + 2 x - x^{2} d x

y = \frac{6 x}{x ^{2} + 1}, (0, 0)

\int_{0}^{4} (3 x - \frac{x ^{3}}{4}) d x

\int_{0}^{πa} x^{2} sin^{2} (x) d x

What is the derivative of f(x)=ln(x^6e^x) ?
The derivative of f(x)=ln(x^6e^x) is 6/x+1
What is the first derivative of f(x)=ln(x^6e^x) ?
The first derivative of f(x)=ln(x^6e^x) is 6/x+1