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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{'''}} - 6 y^{^{''}} - y^{^{'}} + 6 y = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 3 e^{- 5 t}

\int_{- 6}^{6} 36 - x^{2} d x

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\int 9 (x + 1)^{2} ln (x + 1) d x

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