derivative of (x^2+7\sqrt[3]{x^2+2})

Lösung

\frac{d}{d x} ((x^{2} + 7) 3 x^{2} + 2)

2 x 3 x^{2} + 2 + \frac{2 x ( x ^{2} + 7 )}{3 ( x ^{2} + 2 ) ^{\frac{2}{3}}}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 7) 3 x^{2} + 2)

Wende die Produktregel an:

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

f = x^{2} + 7, g = 3 x^{2} + 2

= \frac{d}{d x} (x^{2} + 7) 3 x^{2} + 2 + \frac{d}{d x} (3 x^{2} + 2) (x^{2} + 7)

\frac{d}{d x} (x^{2} + 7) = 2 x

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

= 2 x 3 x^{2} + 2 + \frac{2 x}{3 ( x ^{2} + 2 ) ^{\frac{2}{3}}} (x^{2} + 7)

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x 3 x^{2} + 2 + \frac{2 x ( x ^{2} + 7 )}{3 ( x ^{2} + 2 ) ^{\frac{2}{3}}}

\int - 4 sin (4 t) + 1 d t

x \to + 4 lim (9 x + ∣ x - 4 ∣)

d er i v a t i v e - sin^{3} (x)

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

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