derivative of 4x^2sqrt(5x+1)

Lösung

\frac{d}{d x} (4 x^{2} 5 x + 1)

\frac{2 ( 25 x ^{2} + 4 x )}{5 x + 1}

Schritte zur Lösung

\frac{d}{d x} (4 x^{2} 5 x + 1)

Entferne die Konstante:

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

= 4 \frac{d}{d x} (x^{2} 5 x + 1)

Wende die Produktregel an:

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

f = x^{2}, g = 5 x + 1

= 4 (\frac{d}{d x} (x^{2}) 5 x + 1 + \frac{d}{d x} (5 x + 1) x^{2})

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

\frac{d}{d x} (5 x + 1) = \frac{5}{2 5 x + 1}

= 4 (2 x 5 x + 1 + \frac{5}{2 5 x + 1} x^{2})

Vereinfache

4 (2 x 5 x + 1 + \frac{5}{2 5 x + 1} x^{2}) : \frac{2 ( 25 x ^{2} + 4 x )}{5 x + 1}

= \frac{2 ( 25 x ^{2} + 4 x )}{5 x + 1}

\int \frac{5}{4 sin ( x ) + 3 cos ( x )} d x

x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0, y (1) = 0, y^{^{'}} (1) = - 4

d er i v a t i v e \frac{2}{4 x ^{3}}

\frac{d}{d x} (sin (ln (4) x^{2}))

d er i v a t i v e y = x 400 - x^{2}