What is the derivative of (2log_{2}(x))/(ln(2)x) ?

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

What is the first derivative of (2log_{2}(x))/(ln(2)x) ?

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

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derivative of

\frac{2 lo g _{2} ( x )}{ln ( 2 ) x}

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

Solution steps

\frac{d}{d x} (\frac{2 lo g _{2} ( x )}{ln ( 2 ) x})

Take the constant out:

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

= \frac{2}{ln ( 2 )} \frac{d}{d x} (\frac{lo g _{2} ( x )}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{6 x ^{2} + 8 x + 6}{x}

\frac{d ^{2}}{d x ^{2}} (15 e^{\frac{1}{x}})

\int cos^{3} (θ) sin (θ) d θ

x y^{^{''}} + 2 y^{^{'}} = 0

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

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