What is the derivative of 2ln(x^2+1) ?

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

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

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

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derivative of

2 ln (x^{2} + 1)

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

2 + x

\frac{1}{( 1 + x )}

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

x^{6} + x^{3} + 2

\frac{5 x}{2}

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