derivative 1/2 x^2sqrt(49-x^2)

Lösung

ableitung von

\frac{1}{2} x^{2} 49 - x^{2}

\frac{98 x - 3 x ^{3}}{2 49 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2} x^{2} 49 - x^{2})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (x^{2} 49 - x^{2})

Wende die Produktregel an:

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

f = x^{2}, g = 49 - x^{2}

= \frac{1}{2} (\frac{d}{d x} (x^{2}) 49 - x^{2} + \frac{d}{d x} (49 - x^{2}) x^{2})

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

\frac{d}{d x} (49 - x^{2}) = - \frac{x}{49 - x ^{2}}

= \frac{1}{2} (2 x 49 - x^{2} + (- \frac{x}{49 - x ^{2}}) x^{2})

Vereinfache

\frac{1}{2} (2 x 49 - x^{2} + (- \frac{x}{49 - x ^{2}}) x^{2}) : \frac{98 x - 3 x ^{3}}{2 49 - x ^{2}}

= \frac{98 x - 3 x ^{3}}{2 49 - x ^{2}}

\int cos^{5} (x) sin (2 x) d x

\frac{\partial}{\partial x} (x^{2} - 2 x y + 6 y^{2} + x - 5 y)

\int y^{5} d y

x \to 0 lim (\frac{e ^{x} + 1}{x})

t an g e n t 3 x^{2} - 5 x