derivative y=6x(2x+1)^2+(2x+1)^3

Lösung

ableitung von

y = 6 x (2 x + 1)^{2} + (2 x + 1)^{3}

96 x^{2} + 72 x + 12

Schritte zur Lösung

\frac{d}{d x} (6 x (2 x + 1)^{2} + (2 x + 1)^{3})

Vereinfache

6 x (2 x + 1)^{2} + (2 x + 1)^{3} : 32 x^{3} + 36 x^{2} + 12 x + 1

= \frac{d}{d x} (32 x^{3} + 36 x^{2} + 12 x + 1)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (32 x^{3}) + \frac{d}{d x} (36 x^{2}) + \frac{d}{d x} (12 x) + \frac{d}{d x} (1)

\frac{d}{d x} (32 x^{3}) = 96 x^{2}

\frac{d}{d x} (36 x^{2}) = 72 x

\frac{d}{d x} (12 x) = 12

\frac{d}{d x} (1) = 0

= 96 x^{2} + 72 x + 12 + 0

Vereinfache

= 96 x^{2} + 72 x + 12

y^{^{''}} - 10 y^{^{'}} + 29 y = 0

\frac{d}{d x} (\frac{1}{x} + \frac{3}{x ^{2}} + \frac{2}{x ^{3}})

x \to \infty lim (co d s)

\int_{1}^{e} x (ln (x))^{2} d x

\frac{d}{d x} (cos (e^{x^{4} s i n (x)}))