derivative 2x^4sqrt(25-x^2)

Lösung

ableitung von

2 x^{4} 25 - x^{2}

\frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (2 x^{4} 25 - x^{2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (x^{4} 25 - x^{2})

Wende die Produktregel an:

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

f = x^{4}, g = 25 - x^{2}

= 2 (\frac{d}{d x} (x^{4}) 25 - x^{2} + \frac{d}{d x} (25 - x^{2}) x^{4})

\frac{d}{d x} (x^{4}) = 4 x^{3}

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

= 2 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4})

Vereinfache

2 (4 x^{3} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{4}) : \frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

= \frac{2 ( - 5 x ^{5} + 100 x ^{3} )}{25 - x ^{2}}

y^{^{''''}} + 1 = 0

\frac{\partial}{\partial x} (\frac{4}{x y} - x^{2} + 3 y^{2})

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

d er i v a t i v e 5 x^{\frac{7}{4}} + 5 x^{\frac{1}{3}} - 2

(2 x + t) \frac{d x}{d t} + x - 2 t = 0