What is the derivative of log_{e}(1/x) ?

The derivative of log_{e}(1/x) is -1/x

What is the first derivative of log_{e}(1/x) ?

The first derivative of log_{e}(1/x) is -1/x

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\frac{d}{d x} (lo g_{e} (\frac{1}{x}))

- \frac{1}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (\frac{1}{x}))

Simplify

lo g_{e} (\frac{1}{x}) : - ln (x)

= \frac{d}{d x} (- ln (x))

Take the constant out:

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

= - \frac{d}{d x} (ln (x))

Apply the common derivative:

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= - \frac{1}{x}

\int \frac{9 x ^{3}}{x ^{2} + 9} d x

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

y^{^{'}} + y = x^{2}

(17 + x^{2}) y^{^{'}} - 2 x y = 0

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

What is the derivative of log_{e}(1/x) ?
The derivative of log_{e}(1/x) is -1/x
What is the first derivative of log_{e}(1/x) ?
The first derivative of log_{e}(1/x) is -1/x