derivative of (1+x^2(1+sqrt(x)))

Lösung

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

\frac{5 x ^{2} + 4 x x + 1}{2 x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = 1 + x^{2}, g = 1 + x

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

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

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

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

Vereinfache

2 x (1 + x) + \frac{1}{2 x} (1 + x^{2}) : \frac{5 x ^{2} + 4 x x + 1}{2 x}

= \frac{5 x ^{2} + 4 x x + 1}{2 x}

x \to - 1 lim (\frac{4 x + 3}{2 x + 1})

\int 10 e^{\frac{x}{20}} d x

\int \frac{1 - 2 y}{y} d y

in v erse l a pl a ce \frac{s + 1}{( s + 1 ) ^{2} + 5}

\frac{d}{d x} (6 sin (x) - 6 x cos (x))