What is the solution for derivative of y=log_{2}(x) ?

The solution for derivative of y=log_{2}(x) is y=xlog_{2}(x)-x/(ln(2))+c_{1}

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Find the Derivative - d/dx y = log base 2 of x

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

y = x lo g_{2} (x) - \frac{x}{ln ( 2 )} + c_{1}

Solution steps

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

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int lo g_{2} (x) d x

\int lo g_{2} (x) d x = x lo g_{2} (x) - \frac{1}{ln ( 2 )} x + c_{1}

y = x lo g_{2} (x) - \frac{1}{ln ( 2 )} x + c_{1}

Simplify

y = x lo g_{2} (x) - \frac{x}{ln ( 2 )} + c_{1}

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

\int (\frac{( x ^{3} )}{( x ^{4} - 5 )}) d x, u = x^{4} - 5

x \to 1 - lim (\frac{( x - 1 )}{( x ^{2} - 4 )})

(- 3, 3), (5, 9)

x \to - \infty lim (\frac{( x ^{4} - 1 )}{( x ^{3} - 1 )})

What is the solution for derivative of y=log_{2}(x) ?
The solution for derivative of y=log_{2}(x) is y=xlog_{2}(x)-x/(ln(2))+c_{1}