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Beliebt Rechnen >

derivative of xy+ln(x/y)

Lösung

\frac{d}{d x} (x y + ln (\frac{x}{y}))

Lösung

y + x \frac{d y}{d x} + \frac{y - x \frac{d y}{d x}}{x y}

Schritte zur Lösung

\frac{d}{d x} (x y + ln (\frac{x}{y}))

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x y) + \frac{d}{d x} (ln (\frac{x}{y}))

\frac{d}{d x} (x y) = y + x \frac{d y}{d x}

\frac{d}{d x} (ln (\frac{x}{y})) = \frac{y - x \frac{d y}{d x}}{x y}

= y + x \frac{d y}{d x} + \frac{y - x \frac{d y}{d x}}{x y}

Beliebte Beispiele

y^{''}-6y^'+9y=0,y(0)=2,y^'(0)= 25/3

y^{^{''}} - 6 y^{^{'}} + 9 y = 0, y (0) = 2, y^{^{'}} (0) = \frac{25}{3}

integral of 2y-5

\int 2 y - 5 d y

derivative ((4x^2+8x+4))/(sqrt(x))

d er i v a t i v e \frac{( 4 x ^{2} + 8 x + 4 )}{x}

integral of sin(8pit)

\int sin (8 π t) d t

xy^'=y+2sqrt(xy)

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