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

The derivative of-ln(4x) is -1/x

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

The first derivative of-ln(4x) is -1/x

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

- \frac{1}{x}

Solution steps

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

Take the constant out:

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

= - \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

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

Simplify

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

= - \frac{1}{x}

\int (- 8 sec (x) tan (x) - 3 sec^{2} (x)) d x

y^{^{''}} + 5 y^{^{'}} - 6 y = (3 x - 1) e^{x}

e^{x^{4}}

x + y = 7

\frac{d}{d x} (x^{c})