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

The derivative of x/(log_{e(x)}) is (ln(x)-1)/(ln^2(x))

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

The first derivative of x/(log_{e(x)}) is (ln(x)-1)/(ln^2(x))

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\frac{d}{d x} (\frac{x}{lo g _{e} ( x )})

\frac{ln ( x ) - 1}{ln ^{2} ( x )}

Solution steps

\frac{d}{d x} (\frac{x}{lo g _{e} ( x )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} lo g _{e} ( x ) - \frac{d}{d x} ( lo g _{e} ( x ) ) x}{( lo g _{e} ( x ) ) ^{2}}

\frac{d x}{d x} = 1

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

= \frac{1 \cdot lo g _{e} ( x ) - \frac{1}{x} x}{( lo g _{e} ( x ) ) ^{2}}

Simplify

\frac{1 \cdot lo g _{e} ( x ) - \frac{1}{x} x}{lo g _{e} ( x ) ^{2}} : \frac{ln ( x ) - 1}{ln ^{2} ( x )}

= \frac{ln ( x ) - 1}{ln ^{2} ( x )}

\frac{d}{d x} (b e^{- x})

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

h \to 0 lim (\frac{\frac{2}{1 + h} - 2}{h})

- 7 x^{4} + 7 x^{3} - x^{2} + x

\int \frac{sec ( 3 x )}{cot ( 3 x )} d x

What is the derivative of x/(log_{e(x)}) ?
The derivative of x/(log_{e(x)}) is (ln(x)-1)/(ln^2(x))
What is the first derivative of x/(log_{e(x)}) ?
The first derivative of x/(log_{e(x)}) is (ln(x)-1)/(ln^2(x))