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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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