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Beliebt Rechnen >

derivative of yln(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y, g = ln (x)

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

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

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

\frac{1}{x} y = \frac{y}{x}

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

Beliebte Beispiele

tangent 6cos(t),\at t=-pi/4

t an g e n t 6 cos (t), at t = - \frac{π}{4}

inverselaplace 2s+1

in v erse l a pl a ce 2 s + 1

tangent f(x)=x^4-4x^3+2x^2-6,\at x=1

t an g e n t f (x) = x^{4} - 4 x^{3} + 2 x^{2} - 6, at x = 1

integral of (x^2)/(x^2+x+12)

\int \frac{x ^{2}}{x ^{2} + x + 12} d x

x y \frac{d y}{d x} = 7