What is the derivative of 3ln(4x) ?

The derivative of 3ln(4x) is 3/x

What is the first derivative of 3ln(4x) ?

The first derivative of 3ln(4x) is 3/x

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\frac{d}{d x} (3 ln (4 x))

\frac{3}{x}

Solution steps

\frac{d}{d x} (3 ln (4 x))

Take the constant out:

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

= 3 \frac{d}{d x} (ln (4 x))

Apply the chain rule:

\frac{1}{4 x} \frac{d}{d x} (4 x)

= \frac{1}{4 x} \frac{d}{d x} (4 x)

\frac{d}{d x} (4 x) = 4

= 3 \cdot \frac{1}{4 x} \cdot 4

Simplify

3 \cdot \frac{1}{4 x} \cdot 4 : \frac{3}{x}

= \frac{3}{x}

\int_{1}^{3} (4 x - 3)^{2} - (x^{2})^{2} d x

\int \frac{6 x ^{2} + 8}{x ^{3} + 4 x} d x

\frac{d y}{d x} + \frac{1}{x} y = x y^{2}

\frac{d y}{d x} + y = e^{7 x}

y^{^{'}} - \frac{5}{x} y = \frac{y ^{5}}{x ^{18}}

What is the derivative of 3ln(4x) ?
The derivative of 3ln(4x) is 3/x
What is the first derivative of 3ln(4x) ?
The first derivative of 3ln(4x) is 3/x