What is the derivative of 5ln(x^3) ?

The derivative of 5ln(x^3) is (15)/x

What is the first derivative of 5ln(x^3) ?

The first derivative of 5ln(x^3) is (15)/x

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\frac{d}{d x} (5 ln (x^{3}))

\frac{15}{x}

Solution steps

\frac{d}{d x} (5 ln (x^{3}))

Take the constant out:

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

= 5 \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}

= 5 \cdot \frac{1}{x ^{3}} \cdot 3 x^{2}

Simplify

5 \cdot \frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{15}{x}

= \frac{15}{x}

What is the derivative of 5ln(x^3) ?
The derivative of 5ln(x^3) is (15)/x
What is the first derivative of 5ln(x^3) ?
The first derivative of 5ln(x^3) is (15)/x