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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} ((2 x - 5)^{4}) = 8 (2 x - 5)^{3}

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

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

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

y^{^{''}} - 5 y^{^{'}} + 4 y = 8 e^{x}

t an g e n t f (x) = - x^{2} + 16 x + 63, at x = 2

\int ln (4 x) d x

\frac{d}{d x} (\frac{1}{1 - cos ( x )})