What is the derivative of 3ln(x^3) ?

The derivative of 3ln(x^3) is 9/x

What is the first derivative of 3ln(x^3) ?

The first derivative of 3ln(x^3) is 9/x

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

\frac{9}{x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 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}

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

Simplify

3 \cdot \frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{9}{x}

= \frac{9}{x}

y = x^{2} + x, at x = 1

\frac{d}{d x} (arctan (\frac{( a ^{2} - x ^{3} )}{b ^{2}}))

\frac{d}{d x} (\frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6})

\int 1 + (4 x)^{2} d x

\frac{d}{d t} (2 t e^{- t})

What is the derivative of 3ln(x^3) ?
The derivative of 3ln(x^3) is 9/x
What is the first derivative of 3ln(x^3) ?
The first derivative of 3ln(x^3) is 9/x