What is the derivative of log_{10}(|3x|) ?

The derivative of log_{10}(|3x|) is 1/(ln(10)x)

What is the first derivative of log_{10}(|3x|) ?

The first derivative of log_{10}(|3x|) is 1/(ln(10)x)

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derivative of

lo g_{10} (∣ 3 x ∣)

\frac{1}{ln ( 10 ) x}

Solution steps

\frac{d}{d x} (lo g_{10} (∣ 3 x ∣))

Simplify

lo g_{10} (∣ 3 x ∣) : lo g_{10} (3 ∣ x ∣)

= \frac{d}{d x} (lo g_{10} (3 ∣ x ∣))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

= \frac{d}{d x} (\frac{ln ( 3 ∣ x ∣ )}{ln ( 10 )})

Take the constant out:

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

= \frac{1}{ln ( 10 )} \frac{d}{d x} (ln (3 ∣ x ∣))

Apply the chain rule:

\frac{1}{3 ∣ x ∣} \frac{d}{d x} (3 ∣ x ∣)

= \frac{1}{3 ∣ x ∣} \frac{d}{d x} (3 ∣ x ∣)

\frac{d}{d x} (3 ∣ x ∣) = \frac{3 x}{∣ x ∣}

= \frac{1}{ln ( 10 )} \cdot \frac{1}{3 ∣ x ∣} \cdot \frac{3 x}{∣ x ∣}

Simplify

\frac{1}{ln ( 10 )} \cdot \frac{1}{3 ∣ x ∣} \cdot \frac{3 x}{∣ x ∣} : \frac{1}{ln ( 10 ) x}

= \frac{1}{ln ( 10 ) x}

2^{3} x

y = x^{2} e^{2}

4 y^{2} - 6 y + 5

lo g_{10} (x^{2} + a^{2})

x^{2} sec (x)

What is the derivative of log_{10}(|3x|) ?
The derivative of log_{10}(|3x|) is 1/(ln(10)x)
What is the first derivative of log_{10}(|3x|) ?
The first derivative of log_{10}(|3x|) is 1/(ln(10)x)