derivative (2x^2+1)(x-3)^2

Lösung

ableitung von

(2 x^{2} + 1) (x - 3)^{2}

8 x^{3} - 36 x^{2} + 38 x - 6

Schritte zur Lösung

\frac{d}{d x} ((2 x^{2} + 1) (x - 3)^{2})

Wende die Produktregel an:

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

f = 2 x^{2} + 1, g = (x - 3)^{2}

= \frac{d}{d x} (2 x^{2} + 1) (x - 3)^{2} + \frac{d}{d x} ((x - 3)^{2}) (2 x^{2} + 1)

\frac{d}{d x} (2 x^{2} + 1) = 4 x

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

= 4 x (x - 3)^{2} + 2 (x - 3) (2 x^{2} + 1)

Vereinfache

4 x (x - 3)^{2} + 2 (x - 3) (2 x^{2} + 1) : 8 x^{3} - 36 x^{2} + 38 x - 6

= 8 x^{3} - 36 x^{2} + 38 x - 6

\int 8 sin^{3} (x) d x

4 x y d x + (x^{2} + 1) d y = 0

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

\frac{\partial}{\partial x} (8 e^{x - y})

\frac{\partial}{\partial x} (e^{x^{2} + y})