What is the derivative of (10log_{4}(x)/x) ?

The derivative of (10log_{4}(x)/x) is (5(-2ln(2)log_{4}(x)+1))/(ln(2)x^2)

What is the first derivative of (10log_{4}(x)/x) ?

The first derivative of (10log_{4}(x)/x) is (5(-2ln(2)log_{4}(x)+1))/(ln(2)x^2)

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\frac{d}{d x} (\frac{10 lo g _{4} ( x )}{x})

\frac{5 ( - 2 ln ( 2 ) lo g _{4} ( x ) + 1 )}{ln ( 2 ) x ^{2}}

Solution steps

\frac{d}{d x} (\frac{10 lo g _{4} ( x )}{x})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{lo g _{4} ( x )}{x})

Apply the Quotient Rule:

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

= 10 \cdot \frac{\frac{d}{d x} ( lo g _{4} ( x ) ) x - \frac{d x}{d x} lo g _{4} ( x )}{x ^{2}}

\frac{d}{d x} (lo g_{4} (x)) = \frac{1}{2 ln ( 2 ) x}

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

= 10 \cdot \frac{\frac{1}{2 l n ( 2 ) x} x - 1 \cdot lo g _{4} ( x )}{x ^{2}}

Simplify

10 \cdot \frac{\frac{1}{2 l n ( 2 ) x} x - 1 \cdot lo g _{4} ( x )}{x ^{2}} : \frac{5 ( - 2 ln ( 2 ) lo g _{4} ( x ) + 1 )}{ln ( 2 ) x ^{2}}

= \frac{5 ( - 2 ln ( 2 ) lo g _{4} ( x ) + 1 )}{ln ( 2 ) x ^{2}}

x \to \infty lim (\frac{6 ^{x + 1}}{7 ^{x - 1}})

\int (x - 3) sin (π x) d x

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

\frac{\partial}{\partial x} (ln (x + 4 y + 7 z))

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

What is the derivative of (10log_{4}(x)/x) ?
The derivative of (10log_{4}(x)/x) is (5(-2ln(2)log_{4}(x)+1))/(ln(2)x^2)
What is the first derivative of (10log_{4}(x)/x) ?
The first derivative of (10log_{4}(x)/x) is (5(-2ln(2)log_{4}(x)+1))/(ln(2)x^2)