derivative y=2x^2sqrt(25-x^2)

Lösung

ableitung von

y = 2 x^{2} 25 - x^{2}

\frac{2 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{2} 25 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x^{2} 25 - x^{2})

Wende die Produktregel an:

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

f = x^{2}, g = 25 - x^{2}

= 2 (\frac{d}{d x} (x^{2}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{2})

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

\frac{d}{d x} (25 - x^{2}) = - \frac{x}{25 - x ^{2}}

= 2 (2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2})

Vereinfache

2 (2 x 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{2}) : \frac{2 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

= \frac{2 ( - 3 x ^{3} + 50 x )}{25 - x ^{2}}

y^{^{'}} = x y - y

\int \frac{2 x}{x ^{2} + 2} d x

2 y^{^{''}} + 5 y^{^{'}} - 3 y = 0, y (0) = 3, y^{^{'}} (0) = 19

d er i v a t i v e f (x) = \frac{7}{8 t ^{4}}

t an g e n t f (x) = 2 x^{3} - x^{2} + 2, at x = 1