derivative of 4x^4+x^3-(9x^2/2+8x)

Lösung

\frac{d}{d x} (4 x^{4} + x^{3} - \frac{9 x ^{2}}{2} + 8 x)

16 x^{3} + 3 x^{2} - 9 x + 8

Schritte zur Lösung

\frac{d}{d x} (4 x^{4} + x^{3} - \frac{9 x ^{2}}{2} + 8 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (4 x^{4}) + \frac{d}{d x} (x^{3}) - \frac{d}{d x} (\frac{9 x ^{2}}{2}) + \frac{d}{d x} (8 x)

\frac{d}{d x} (4 x^{4}) = 16 x^{3}

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

\frac{d}{d x} (\frac{9 x ^{2}}{2}) = 9 x

\frac{d}{d x} (8 x) = 8

= 16 x^{3} + 3 x^{2} - 9 x + 8

t a y l or sin (π x), \frac{1}{2}

(cos^{2} (t))^{^{'}}

\frac{d}{d x} (9 x^{7} + 3 x^{5} - 6 x^{6} - 2 x^{4})

\frac{d}{d x} (5 x^{2} + 7 x - 6)

d er i v a t i v e 10 x \cdot e^{x}