derivative f(x)=x^2*(x^3+2)

Lösung

ableitung von

f (x) = x^{2} \cdot (x^{3} + 2)

5 x^{4} + 4 x

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= 2 x (x^{3} + 2) + 3 x^{2} x^{2}

Vereinfache

2 x (x^{3} + 2) + 3 x^{2} x^{2} : 5 x^{4} + 4 x

= 5 x^{4} + 4 x

\frac{d y}{d x} = \frac{16 x}{e ^{y}}

y^{^{''}} + 4 y = 12 sin (2 x)

d er i v a t i v e f (x) = \frac{4}{3 x ^{2}} + \frac{1}{x ^{2.1}}

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

x \to 4 - lim (\frac{6 x}{x - 4})