derivative of (4pix+3x^6/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{4 π x + 3 x ^{6}}{x})

\frac{4 π + 33 x ^{5}}{2 x}

Schritte zur Lösung

\frac{d}{d x} (\frac{4 π x + 3 x ^{6}}{x})

Vereinfache

\frac{4 π x + 3 x ^{6}}{x} : x (4 π + 3 x^{5})

= \frac{d}{d x} (x (4 π + 3 x^{5}))

Wende die Produktregel an:

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

f = x, g = 4 π + 3 x^{5}

= \frac{d}{d x} (x) (4 π + 3 x^{5}) + \frac{d}{d x} (4 π + 3 x^{5}) x

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

\frac{d}{d x} (4 π + 3 x^{5}) = 15 x^{4}

= \frac{1}{2 x} (4 π + 3 x^{5}) + 15 x^{4} x

Vereinfache

\frac{1}{2 x} (4 π + 3 x^{5}) + 15 x^{4} x : \frac{4 π + 33 x ^{5}}{2 x}

= \frac{4 π + 33 x ^{5}}{2 x}

x \to 0 lim (\frac{7}{x} - \frac{7}{x ^{2} + x})

d er i v a t i v e (2 a + 1)^{2}

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

\int_{1}^{\infty} x^{- 2} d x

\frac{\partial}{\partial x} (arctan (\frac{x}{2}))