d/(dh)(({V}(h))((3h^2+4)^{3/2}-8))

Lösung

\frac{d}{d h} ((V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8))

\frac{d}{d h} (V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8) + 9 h (3 h^{2} + 4)^{\frac{1}{2}} V (h)

Schritte zur Lösung

\frac{d}{d h} ((V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8))

Wende die Produktregel an:

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

f = V (h), g = (3 h^{2} + 4)^{\frac{3}{2}} - 8

= \frac{d}{d h} (V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8) + \frac{d}{d h} ((3 h^{2} + 4)^{\frac{3}{2}} - 8) V (h)

\frac{d}{d h} ((3 h^{2} + 4)^{\frac{3}{2}} - 8) = 9 h (3 h^{2} + 4)^{\frac{1}{2}}

= \frac{d}{d h} (V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8) + 9 h (3 h^{2} + 4)^{\frac{1}{2}} V (h)

e x p an d \frac{5 ( 9 + 201 )}{3}

e x p an d \frac{4000}{( t + 2 ) ^{2}}

e x p an d (x + 6) e^{\frac{1}{x}}

e x p an d (9 e^{3 t}) (18 e^{3 t} t + 12 e^{3 t})

e x p an d \frac{( x + 2 ) ^{3}}{6}