derivative of xsqrt(100-x^2)

Lösung

\frac{d}{d x} (x 100 - x^{2})

\frac{- 2 x ^{2} + 100}{100 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (x 100 - x^{2})

Wende die Produktregel an:

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

f = x, g = 100 - x^{2}

= \frac{d x}{d x} 100 - x^{2} + \frac{d}{d x} (100 - x^{2}) x

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

\frac{d}{d x} (100 - x^{2}) = - \frac{x}{100 - x ^{2}}

= 1 \cdot 100 - x^{2} + (- \frac{x}{100 - x ^{2}}) x

Vereinfache

1 \cdot 100 - x^{2} + (- \frac{x}{100 - x ^{2}}) x : \frac{- 2 x ^{2} + 100}{100 - x ^{2}}

= \frac{- 2 x ^{2} + 100}{100 - x ^{2}}

\int \frac{1}{x ^{5}} - \frac{1}{x} d x

x^{^{''}} - 8 x^{^{'}} + 17 x = 0

\frac{d}{d x} (e^{\frac{x}{( x - 6 )}})

\frac{d}{d x} (ln (1 - \frac{3}{x}))

x \to 2 lim (\frac{x ^{2} - 2 x}{x})