derivative 3x^3sqrt(25-x^2)

Lösung

ableitung von

3 x^{3} 25 - x^{2}

\frac{3 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x^{3}, g = 25 - x^{2}

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

Vereinfache

3 (3 x^{2} 25 - x^{2} + (- \frac{x}{25 - x ^{2}}) x^{3}) : \frac{3 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

= \frac{3 ( - 4 x ^{4} + 75 x ^{2} )}{25 - x ^{2}}

\int_{6}^{8} \frac{70}{( x - 6 ) ^{3}} d x

t a y l or 1 - 3 x^{2}

f^{^{'}} (x) = f (x) (1 - f (x))

d er i v a t i v e f (x) = 200 + \frac{7}{x} + \frac{x ^{2}}{7}

y^{^{'}} = x (9 - y)