What is the derivative of ln(1+x^3) ?

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

What is the first derivative of ln(1+x^3) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{1 + x ^{3}} \cdot 3 x^{2}

Simplify

\frac{1}{1 + x ^{3}} \cdot 3 x^{2} : \frac{3 x ^{2}}{1 + x ^{3}}

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

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