What is the derivative of ln(2pix^2) ?

The derivative of ln(2pix^2) is 2/x

What is the first derivative of ln(2pix^2) ?

The first derivative of ln(2pix^2) is 2/x

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\frac{d}{d x} (ln (2 π x^{2}))

\frac{2}{x}

Solution steps

\frac{d}{d x} (ln (2 π x^{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (2 π x^{2}) = 4 π x

= \frac{1}{2 π x ^{2}} \cdot 4 π x

Simplify

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

= \frac{2}{x}

\int \frac{e ^{6 x}}{e ^{6 x} sin ^{2} ( 4 x )} d x

x \to 2 lim ((\frac{1}{x})^{3})

\frac{d}{d x} (\frac{3}{8} x^{\frac{2}{3}})

\frac{d}{d x} (\frac{2}{x - 3})

\frac{d}{d x} ((\frac{x ^{2} + 1}{x ^{2} - 1})^{3})

What is the derivative of ln(2pix^2) ?
The derivative of ln(2pix^2) is 2/x
What is the first derivative of ln(2pix^2) ?
The first derivative of ln(2pix^2) is 2/x