derivative 7x^5(x^3-6x)

Lösung

ableitung von

7 x^{5} (x^{3} - 6 x)

7 (8 x^{7} - 36 x^{5})

Schritte zur Lösung

\frac{d}{d x} (7 x^{5} (x^{3} - 6 x))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (x^{5} (x^{3} - 6 x))

Wende die Produktregel an:

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

f = x^{5}, g = x^{3} - 6 x

= 7 (\frac{d}{d x} (x^{5}) (x^{3} - 6 x) + \frac{d}{d x} (x^{3} - 6 x) x^{5})

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

\frac{d}{d x} (x^{3} - 6 x) = 3 x^{2} - 6

= 7 (5 x^{4} (x^{3} - 6 x) + (3 x^{2} - 6) x^{5})

Multipliziere aus

5 x^{4} (x^{3} - 6 x) + (3 x^{2} - 6) x^{5} : 8 x^{7} - 36 x^{5}

= 7 (8 x^{7} - 36 x^{5})

d er i v a t i v e \frac{x - 6}{x - 6}

\frac{\partial}{\partial x} (5 x^{2} y - 2 x + 3 y^{3})

\int \frac{e ^{4 x}}{1 + e ^{8 x}} d x

t an g e n t f (x) = x^{2} + 11, at x = 5

\frac{d}{d x} (\frac{1}{x} - 3 sin (x))