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

- \frac{2}{x}

Solution steps

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

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

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

= 1 \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}) = - \frac{14}{x ^{3}}

= 1 \cdot \frac{1}{7 x ^{- 2}} (- \frac{14}{x ^{3}})

Simplify

1 \cdot \frac{1}{7 x ^{- 2}} (- \frac{14}{x ^{3}}) : - \frac{2}{x}

= - \frac{2}{x}

\frac{d}{d x} (\frac{x}{x ^{2} + 5})

\int sin^{3} (6 x) d x

ln (2 e^{- t} sin (t))

f (x) = x^{2} + 3 x + 5

\frac{\partial}{\partial y} (e^{- y})

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