derivative of (2x^2-2xle{f}(x,t)t(x^2-3))

Lösung

\frac{d}{d x} ((2 x^{2} - 2 x) l e f (x, t) t (x^{2} - 3))

l e t ((4 x - 2) f (x, t) (x^{2} - 3) + (\frac{d}{d x} (f (x, t)) (x^{2} - 3) + 2 x f (x, t)) (2 x^{2} - 2 x))

Schritte zur Lösung

\frac{d}{d x} ((2 x^{2} - 2 x) l e f (x, t) t (x^{2} - 3))

Behandle

l, t

als Konstante

Entferne die Konstante:

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

= l e t \frac{d}{d x} ((2 x^{2} - 2 x) f (x, t) (x^{2} - 3))

Wende die Produktregel an:

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

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

= l e t (\frac{d}{d x} (2 x^{2} - 2 x) f (x, t) (x^{2} - 3) + \frac{d}{d x} (f (x, t) (x^{2} - 3)) (2 x^{2} - 2 x))

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

\frac{d}{d x} (f (x, t) (x^{2} - 3)) = \frac{d}{d x} (f (x, t)) (x^{2} - 3) + 2 x f (x, t)

= l e t ((4 x - 2) f (x, t) (x^{2} - 3) + (\frac{d}{d x} (f (x, t)) (x^{2} - 3) + 2 x f (x, t)) (2 x^{2} - 2 x))

d er i v a t i v e f (x) = (2 + 5 x)^{2}

x \to 0 + lim (\frac{1}{x} - \frac{1}{x ^{2} + x})

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

\int_{0}^{2} 8 e^{- 3 x} d x

x \to - 3 lim (9 - x^{2})