derivative of (5x^6/2+(12)/(7x^5)-x)

Lösung

\frac{d}{d x} (\frac{5 x ^{6}}{2} + \frac{12}{7 x ^{5}} - x)

15 x^{5} - \frac{60}{7 x ^{6}} - 1

Schritte zur Lösung

\frac{d}{d x} (\frac{5 x ^{6}}{2} + \frac{12}{7 x ^{5}} - x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{5 x ^{6}}{2}) + \frac{d}{d x} (\frac{12}{7 x ^{5}}) - \frac{d x}{d x}

\frac{d}{d x} (\frac{5 x ^{6}}{2}) = 15 x^{5}

\frac{d}{d x} (\frac{12}{7 x ^{5}}) = - \frac{60}{7 x ^{6}}

\frac{d x}{d x} = 1

= 15 x^{5} - \frac{60}{7 x ^{6}} - 1

\int \frac{4 x}{x - 8} d x

x \to 0 lim (arcsin (1 + 2 x))

\int_{1}^{5} \frac{7}{x ^{2}} d x

\frac{d}{d x} ((5 x + 8)^{3})

\frac{d}{d x} ((\frac{x - 7}{x + 2})^{2})