derivative (x^6-5)sqrt(x)

Lösung

ableitung von

(x^{6} - 5) x

\frac{13 x ^{6} - 5}{2 x}

Schritte zur Lösung

\frac{d}{d x} ((x^{6} - 5) x)

Wende die Produktregel an:

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

f = x^{6} - 5, g = x

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

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

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

= 6 x^{5} x + \frac{1}{2 x} (x^{6} - 5)

Vereinfache

6 x^{5} x + \frac{1}{2 x} (x^{6} - 5) : \frac{13 x ^{6} - 5}{2 x}

= \frac{13 x ^{6} - 5}{2 x}

\frac{d}{d x} (\frac{cos ( x )}{x + 1})

d er i v a t i v e (x - 3) (x + 2) (x + 3)

\int \frac{1 + x ^{2}}{x} d x

d er i v a t i v e 45 + 22 sin (\frac{2 π}{52} (t - 10))

12 y^{^{''}} - 5 y^{^{'}} - 3 y = 0