derivative of xln(4y+sqrt(x+y))

Lösung

\frac{d}{d x} (x ln (4 y) + x + y)

ln (4 y) + \frac{x \frac{d y}{d x}}{y} + \frac{1 + \frac{d y}{d x}}{2 x + y}

Schritte zur Lösung

\frac{d}{d x} (x ln (4 y) + x + y)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (x ln (4 y)) + \frac{d}{d x} (x + y)

\frac{d}{d x} (x ln (4 y)) = ln (4 y) + \frac{x \frac{d y}{d x}}{y}

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

= ln (4 y) + \frac{x \frac{d y}{d x}}{y} + \frac{1 + \frac{d y}{d x}}{2 x + y}

\int 6 x^{\frac{3}{2}} d x

x \to \infty lim (4^{x} + 5)

\frac{d}{d x} (\frac{3}{x ^{2}} + \frac{1}{x})

\int \frac{1}{x ^{2} - 2 x + 10} d x

49 y^{^{''}} + 28 y^{^{'}} + 4 y = 0