derivative of x^4(x^2+1^6)

Lösung

\frac{d}{d x} (x^{4} (x^{2} + 1)^{6})

4 x^{3} (x^{2} + 1)^{6} + 12 x^{5} (x^{2} + 1)^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{4} (x^{2} + 1)^{6})

Wende die Produktregel an:

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

f = x^{4}, g = (x^{2} + 1)^{6}

= \frac{d}{d x} (x^{4}) (x^{2} + 1)^{6} + \frac{d}{d x} ((x^{2} + 1)^{6}) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} ((x^{2} + 1)^{6}) = 12 x (x^{2} + 1)^{5}

= 4 x^{3} (x^{2} + 1)^{6} + 12 x (x^{2} + 1)^{5} x^{4}

12 x (x^{2} + 1)^{5} x^{4} = 12 x^{5} (x^{2} + 1)^{5}

= 4 x^{3} (x^{2} + 1)^{6} + 12 x^{5} (x^{2} + 1)^{5}

\frac{d}{d x} (- \frac{5}{( x + 3 ) ^{3}})

t a y l or \frac{1}{( 7 + x ) 2}

x \to 0 lim (x sin (x))

\int_{0}^{l n (21)} x e^{x} d x

\int \frac{3}{x ( x + 3 )} d x