derivative of 6x^{7/2}+4x^{5/2}+2x

Lösung

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

21 x^{\frac{5}{2}} + 10 x^{\frac{3}{2}} + 2

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (6 x^{\frac{7}{2}}) + \frac{d}{d x} (4 x^{\frac{5}{2}}) + \frac{d}{d x} (2 x)

\frac{d}{d x} (6 x^{\frac{7}{2}}) = 21 x^{\frac{5}{2}}

\frac{d}{d x} (4 x^{\frac{5}{2}}) = 10 x^{\frac{3}{2}}

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

= 21 x^{\frac{5}{2}} + 10 x^{\frac{3}{2}} + 2

d er i v a t i v e f (x) = x + 5 x

in v erse l a pl a ce \frac{e ^{- π s}}{s - 1}

\frac{d}{d x} (2 x^{6})

d er i v a t i v e - 2 t (6 t^{6} - 1)^{6}

l a pl a ce t r an s f or m e^{- 6 t}