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Popular Calculus >

derivative of ln((x^2+1^2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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