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

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= 3 \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}

= 3 (\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}}

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

Vereinfache

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

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

\int \frac{8 x ^{2} + 8 x + 2}{( 4 x ^{2} + 1 ) ^{2}} d x

\int_{1}^{2} \frac{1}{x ^{3} + x} d x

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

\int_{0}^{1} \frac{e ^{x}}{1 + e ^{2 x}} d x

x \to 3 lim (\frac{1}{3} x^{2} - 4 x + 10)