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

The derivative of ln(4x^3+x) is (12x^2+1)/(4x^3+x)

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

The first derivative of ln(4x^3+x) is (12x^2+1)/(4x^3+x)

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derivative of

ln (4 x^{3} + x)

\frac{12 x ^{2} + 1}{4 x ^{3} + x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x^{3} + x) = 12 x^{2} + 1

= \frac{1}{4 x ^{3} + x} (12 x^{2} + 1)

Simplify

\frac{1}{4 x ^{3} + x} (12 x^{2} + 1) : \frac{12 x ^{2} + 1}{4 x ^{3} + x}

= \frac{12 x ^{2} + 1}{4 x ^{3} + x}

What is the derivative of ln(4x^3+x) ?
The derivative of ln(4x^3+x) is (12x^2+1)/(4x^3+x)
What is the first derivative of ln(4x^3+x) ?
The first derivative of ln(4x^3+x) is (12x^2+1)/(4x^3+x)