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

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

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

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

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derivative of

3 ln (5 x)

\frac{3}{x}

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (5 x) = 5

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

Simplify

3 \cdot \frac{1}{5 x} \cdot 5 : \frac{3}{x}

= \frac{3}{x}

x^{2} + 2 x y + x \frac{d y}{d x} = 0

3 x^{4} - 65 x^{3}

\int 2 sec^{4} (x) d x

\int - \frac{5000}{x ^{2}} d x

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

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