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

The derivative of log_{e}(x^3) is 3/x

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

The first derivative of log_{e}(x^3) is 3/x

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

\frac{3}{x}

Solution steps

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

Simplify

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

= \frac{d}{d x} (ln (x^{3}))

Apply the chain rule:

\frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

= \frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= \frac{1}{x ^{3}} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{3}{x}

= \frac{3}{x}

\int_{0}^{2} \frac{1}{8} (x + y) d y

f (x) = e^{2 x} - 1

\int 5 cos^{5} (x) sin^{4} (x) d x

y = x^{3} - 2 x^{2} + 5, at x = 2

ln (π)

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