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

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

\frac{d}{d x} (x + 1) = 1

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

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

Vereinfache

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

\int e^{- \frac{x}{2}} d x

d er i v a t i v e \frac{x ^{2} - 6 x}{x + 1}

a re a y = x^{2} - 2 x, y = x + 4

\frac{d}{d x} (x cos (x) - sin (x) ln (cos (x)))

\frac{d}{d x} (c e^{- 3 x})