derivative y=(x^2+32sqrt(x))/8

Lösung

ableitung von

y = \frac{x ^{2} + 32 x}{8}

\frac{1}{8} (2 x + \frac{16}{x})

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} + 32 x}{8})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{8} \frac{d}{d x} (x^{2} + 32 x)

Wende die Summen-/Differenzregel an:

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

= \frac{1}{8} (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (32 x))

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (32 x) = \frac{16}{x}

= \frac{1}{8} (2 x + \frac{16}{x})

\int (x^{3} - 3 x) d x

\int_{2}^{5} e^{5 x} d x

x \to 1 lim (3 ln (x) + 4)

y^{^{''}} - 6 y^{^{'}} + 25 y = 0

\frac{d y}{d x} = \frac{( y ^{2} - 1 )}{( x ^{2} - 1 )}, y (0) = 1