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

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

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

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

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derivative of

y = ln (3 x^{5})

\frac{5}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{3 x ^{5}} \frac{d}{d x} (3 x^{5})

= \frac{1}{3 x ^{5}} \frac{d}{d x} (3 x^{5})

\frac{d}{d x} (3 x^{5}) = 15 x^{4}

= \frac{1}{3 x ^{5}} \cdot 15 x^{4}

Simplify

\frac{1}{3 x ^{5}} \cdot 15 x^{4} : \frac{5}{x}

= \frac{5}{x}

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