derivative y=(x^6-10)x

Lösung

ableitung von

y = (x^{6} - 10) x

7 x^{6} - 10

Schritte zur Lösung

\frac{d}{d x} ((x^{6} - 10) x)

Wende die Produktregel an:

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

f = x^{6} - 10, g = x

= \frac{d}{d x} (x^{6} - 10) x + \frac{d x}{d x} (x^{6} - 10)

\frac{d}{d x} (x^{6} - 10) = 6 x^{5}

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

= 6 x^{5} x + 1 \cdot (x^{6} - 10)

Vereinfache

6 x^{5} x + 1 \cdot (x^{6} - 10) : 7 x^{6} - 10

= 7 x^{6} - 10

\frac{d y}{d t} = 0.0572 (400 - y), y (0) = 32

y^{^{'}} + \frac{1 - 2 x}{x ^{2}} y - 1 = 0

\frac{\partial}{\partial y} (x y + yz + zy)

d er i v a t i v e f (x) = - \frac{1}{9} (x^{- 9} - x^{18})

\int \frac{1}{16 e ^{- 5 x} + e ^{5 x}} d x