What is the derivative of f(x)=5ln(4x) ?

The derivative of f(x)=5ln(4x) is 5/x

What is the first derivative of f(x)=5ln(4x) ?

The first derivative of f(x)=5ln(4x) is 5/x

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derivative of

f (x) = 5 ln (4 x)

\frac{5}{x}

Solution steps

\frac{d}{d x} (5 ln (4 x))

Take the constant out:

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

= 5 \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

= 5 \cdot \frac{1}{4 x} \cdot 4

Simplify

5 \cdot \frac{1}{4 x} \cdot 4 : \frac{5}{x}

= \frac{5}{x}

f (x) = \frac{x - 5}{( x + 3 ) ^{4}}

\int sin (x) sec^{10} (x) d x

\frac{8}{t ^{8}} - \frac{6}{t ^{6}} + \frac{3}{t}

f (x) = arctan (sin (4 x))

\int \frac{1}{x ^{2} + 2 x + 82} d x

What is the derivative of f(x)=5ln(4x) ?
The derivative of f(x)=5ln(4x) is 5/x
What is the first derivative of f(x)=5ln(4x) ?
The first derivative of f(x)=5ln(4x) is 5/x