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Beliebt Rechnen >

d/(dy)((ln(y))/(2sqrt(y))+1/(sqrt(y)))

Lösung

\frac{d}{d y} (\frac{ln ( y )}{2 y} + \frac{1}{y})

Lösung

- \frac{ln ( y )}{4 y ^{\frac{3}{2}}}

Schritte zur Lösung

\frac{d}{d y} (\frac{ln ( y )}{2 y} + \frac{1}{y})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d y} (\frac{ln ( y )}{2 y}) + \frac{d}{d y} (\frac{1}{y})

\frac{d}{d y} (\frac{ln ( y )}{2 y}) = \frac{2 - ln ( y )}{4 y y}

\frac{d}{d y} (\frac{1}{y}) = - \frac{1}{2 y ^{\frac{3}{2}}}

= \frac{2 - ln ( y )}{4 y y} - \frac{1}{2 y ^{\frac{3}{2}}}

Vereinfache

\frac{2 - ln ( y )}{4 y y} - \frac{1}{2 y ^{\frac{3}{2}}} : - \frac{ln ( y )}{4 y ^{\frac{3}{2}}}

= - \frac{ln ( y )}{4 y ^{\frac{3}{2}}}

Graph

Beliebte Beispiele

limit as x approaches-2 of-10

x \to - 2 lim (- 10)

xy^'+y=y^2,y(1)=-9

x y^{^{'}} + y = y^{2}, y (1) = - 9

derivative of cosh(3x)

\frac{d}{d x} (cosh (3 x))

integral of rsin(r^2)

\int r sin (r^{2}) d r

integral of (2x^2+6)/((x^2-2x+2)^2)

\int \frac{2 x ^{2} + 6}{( x ^{2} - 2 x + 2 ) ^{2}} d x