derivative x(x^2+4)

Lösung

ableitung von

x (x^{2} + 4)

3 x^{2} + 4

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x^{2} + 4

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

\frac{d x}{d x} = 1

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

= 1 \cdot (x^{2} + 4) + 2 xx

Vereinfache

1 \cdot (x^{2} + 4) + 2 xx : 3 x^{2} + 4

= 3 x^{2} + 4

d er i v a t i v e \frac{( x ^{2} - 1 )}{x ^{2} + 1}

\int_{- \infty}^{0} \frac{z}{z ^{4} + 4} d z

5 y^{^{''}} + 4 y^{^{'}} = 0

x \to \infty + lim (sec (x))

\int \frac{( x + 6 )}{5 - 4 x - x ^{2}} d x