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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\frac{d}{d x} (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}

\int x^{3} (8^{- x^{4}}) d x

\frac{d}{d x} (2 x^{3} - 11.7 x^{2} + 17.7 x - 5)

\int \frac{- 3 x ^{3}}{x ^{2} + 9} d x

\frac{d}{d x} (\frac{x y}{z})

\frac{\partial}{\partial x} ((x - y)^{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