derivative of x^2sqrt(4-x)

Lösung

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

\frac{- 5 x ^{2} + 16 x}{2 4 - x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

2 x 4 - x + (- \frac{1}{2 4 - x}) x^{2} : \frac{- 5 x ^{2} + 16 x}{2 4 - x}

= \frac{- 5 x ^{2} + 16 x}{2 4 - x}

x^{^{'}} = 6 - \frac{3}{5} \cdot x

\int e^{x} tan (e^{x}) d x

\frac{d}{d x} (a sin (2 x) + b cos (2 x))

\frac{d}{d x} (3 x^{2} + \frac{8 x}{3} - 2)

x \to 0 lim (- 5 (x - 3) ln (t (x) - 3))