derivative of y=log_{2}(x)

Lösung

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

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

Schritte zur Lösung

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

Wenn

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

dann

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}

Vereinfache

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

d er i v a t i v e \frac{d}{d x} (ln (\frac{1}{x}))

s u b s t i t u t i o n \int (\frac{( x ^{3} )}{( x ^{4} - 5 )}) d x, u = x^{4} - 5

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

s l o p e (- 3, 3), (5, 9)

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