What is the derivative of ln(x^4+1) ?

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

What is the first derivative of ln(x^4+1) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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