derivative of 1/8 xsqrt(64-x^2)

Lösung

\frac{d}{d x} (\frac{1}{8} x 64 - x^{2})

\frac{32 - x ^{2}}{4 - x ^{2} + 64}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{8} x 64 - x^{2})

Entferne die Konstante:

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

= \frac{1}{8} \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}

= \frac{1}{8} (\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}}

= \frac{1}{8} (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x)

Vereinfache

\frac{1}{8} (1 \cdot 64 - x^{2} + (- \frac{x}{64 - x ^{2}}) x) : \frac{32 - x ^{2}}{4 - x ^{2} + 64}

= \frac{32 - x ^{2}}{4 - x ^{2} + 64}

s l o p e in t erce pt (5, - 4), (4, 7)

\int \frac{7}{x 36 - 49 ln ^{2} ( x )} d x

\frac{d}{d x} (x sin (x) + cos (x))

\int 13 + 12 x - x^{2} d x

y^{^{'}} = 2 y + x^{2} + 7