derivative of x^2sqrt(x^2-9)

Lösung

\frac{d}{d x} (x^{2} x^{2} - 9)

\frac{3 x ^{3} - 18 x}{x ^{2} - 9}

Schritte zur Lösung

\frac{d}{d x} (x^{2} x^{2} - 9)

Wende die Produktregel an:

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

f = x^{2}, g = x^{2} - 9

= \frac{d}{d x} (x^{2}) x^{2} - 9 + \frac{d}{d x} (x^{2} - 9) x^{2}

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

\frac{d}{d x} (x^{2} - 9) = \frac{x}{x ^{2} - 9}

= 2 x x^{2} - 9 + \frac{x}{x ^{2} - 9} x^{2}

Vereinfache

2 x x^{2} - 9 + \frac{x}{x ^{2} - 9} x^{2} : \frac{3 x ^{3} - 18 x}{x ^{2} - 9}

= \frac{3 x ^{3} - 18 x}{x ^{2} - 9}

x \to 12 lim (\frac{x ^{3}}{3})

\frac{\partial}{\partial y} (x + y - 320)

\frac{\partial}{\partial x} (x^{4} + y^{3})

t a y l or \frac{1}{1 + x}, 0

n = 1 \sum \infty \frac{- 9 ^{n}}{n ^{4}}