derivative of sqrt(1+2x)-sqrt(1-4x)

Lösung

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

\frac{1}{1 + 2 x} + \frac{2}{1 - 4 x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (1 - 4 x) = - \frac{2}{1 - 4 x}

= \frac{1}{1 + 2 x} - (- \frac{2}{1 - 4 x})

Vereinfache

= \frac{1}{1 + 2 x} + \frac{2}{1 - 4 x}

\int \frac{4}{( x + 1 )} d x

\frac{d}{d x} (ln (e^{s i n (x)} \cdot x^{c o s (x)}))

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

t y^{^{'}} + 4 y = t^{3}, y (2) = 4

\frac{d}{d x} (\frac{w}{1 - 4 x ^{2}})