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 3 x^{2} - 4 x + 2 d x

y^{^{'}} = \frac{y ^{4} + 3}{4 x y ^{3}}

\int \frac{1}{4 e ^{- 7 x} + e ^{7 x}} d x

\frac{\partial}{\partial x} (ln (x) + ln (y))

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

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