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

Lösung

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

8 (2 x - 4)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 4)^{4}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = (2 x - 4)^{4}, g = (x^{2} + x + 1)^{5}

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

\frac{d}{d x} ((2 x - 4)^{4}) = 8 (2 x - 4)^{3}

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

= 8 (2 x - 4)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 4)^{4}

\int \frac{( 5 x + 3 )}{( x ^{2} + 4 x + 7 )} d x

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

k = 1 \sum \infty \frac{k}{k ^{2} + 1}

\int_{0}^{1 - y} 6 x d x

\frac{\partial}{\partial x} (3 (\frac{( 4 + x )}{5 + z})^{2})