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

Lösung

ableitung von

\frac{x ^{2}}{8 + x}

\frac{4 x ( 8 + x ) - x ^{\frac{3}{2}}}{2 ( 8 + x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

\frac{2 x ( 8 + x ) - \frac{1}{2 x} x ^{2}}{( 8 + x ) ^{2}} : \frac{4 x ( 8 + x ) - x ^{\frac{3}{2}}}{2 ( 8 + x ) ^{2}}

= \frac{4 x ( 8 + x ) - x ^{\frac{3}{2}}}{2 ( 8 + x ) ^{2}}

\int \frac{cos ( x )}{sin ( x )} d x

n = 0 \sum \infty \frac{1}{n} - \frac{1}{n + 2}

y^{^{'}} = - 1.5 y

\int cos^{4} (\frac{x}{2}) d x

l a pl a ce t r an s f or m 2 t^{2}