derivative of x^2sqrt(3-4x)

Lösung

\frac{d}{d x} (x^{2} 3 - 4 x)

\frac{- 10 x ^{2} + 6 x}{3 - 4 x}

Schritte zur Lösung

\frac{d}{d x} (x^{2} 3 - 4 x)

Wende die Produktregel an:

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

f = x^{2}, g = 3 - 4 x

= \frac{d}{d x} (x^{2}) 3 - 4 x + \frac{d}{d x} (3 - 4 x) x^{2}

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

\frac{d}{d x} (3 - 4 x) = - \frac{2}{3 - 4 x}

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

Vereinfache

2 x 3 - 4 x + (- \frac{2}{3 - 4 x}) x^{2} : \frac{- 10 x ^{2} + 6 x}{3 - 4 x}

= \frac{- 10 x ^{2} + 6 x}{3 - 4 x}

\frac{\partial}{\partial y} (3 x e^{2 x y})

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

d er i v a t i v e \frac{x}{x - 4}

d er i v a t i v e \frac{- 2 x ^{2} + 9}{9 - x ^{2}}

\int_{7}^{8} (\frac{1}{x ^{2}} - 1) d x