What is the derivative of log_{e}(7x^2) ?

The derivative of log_{e}(7x^2) is 2/x

What is the first derivative of log_{e}(7x^2) ?

The first derivative of log_{e}(7x^2) is 2/x

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derivative of

lo g_{e} (7 x^{2})

\frac{2}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (7 x^{2}))

Simplify

lo g_{e} (7 x^{2}) : ln (7 x^{2})

= \frac{d}{d x} (ln (7 x^{2}))

Apply the chain rule:

\frac{1}{7 x ^{2}} \frac{d}{d x} (7 x^{2})

= \frac{1}{7 x ^{2}} \frac{d}{d x} (7 x^{2})

\frac{d}{d x} (7 x^{2}) = 14 x

= \frac{1}{7 x ^{2}} \cdot 14 x

Simplify

\frac{1}{7 x ^{2}} \cdot 14 x : \frac{2}{x}

= \frac{2}{x}

What is the derivative of log_{e}(7x^2) ?
The derivative of log_{e}(7x^2) is 2/x
What is the first derivative of log_{e}(7x^2) ?
The first derivative of log_{e}(7x^2) is 2/x