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

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

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

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

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derivative of

ln (3 x^{4})

\frac{4}{x}

Solution steps

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

Apply the chain rule:

\frac{1}{3 x ^{4}} \frac{d}{d x} (3 x^{4})

= \frac{1}{3 x ^{4}} \frac{d}{d x} (3 x^{4})

\frac{d}{d x} (3 x^{4}) = 12 x^{3}

= \frac{1}{3 x ^{4}} \cdot 12 x^{3}

Simplify

\frac{1}{3 x ^{4}} \cdot 12 x^{3} : \frac{4}{x}

= \frac{4}{x}

1 - tan^{2} (\frac{x}{2})

\frac{1}{cos ( 2 x )}

5 \cdot sin^{2} (x) - 8 \cdot cos^{5} (x)

\frac{d}{d x} (x^{5} \cdot a + x^{5} \cdot b - a - b)

(x^{2} + 5 x) 5

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