derivative of 2xsqrt(64-x^2)

Lösung

\frac{d}{d x} (2 x 64 - x^{2})

\frac{2 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x 64 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x 64 - x^{2})

Wende die Produktregel an:

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

f = x, g = 64 - x^{2}

= 2 (\frac{d x}{d x} 64 - x^{2} + \frac{d}{d x} (64 - x^{2}) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (64 - x^{2}) = - \frac{x}{64 - x ^{2}}

= 2 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x)

Vereinfache

2 (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x) : \frac{2 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

= \frac{2 ( - 2 x ^{2} + 64 )}{64 - x ^{2}}

x \to - 1 lim (- 1^{3})

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

\int tan^{2} (x) d tan (x) d x

\int 25 - x^{2} d x

z \to 0 lim (\frac{8}{z ^{3}} + \frac{2}{z} + 2)