derivative f(x)=4x^4-3x^{5/2}+2

Lösung

ableitung von

f (x) = 4 x^{4} - 3 x^{\frac{5}{2}} + 2

16 x^{3} - \frac{15 x ^{\frac{3}{2}}}{2}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (3 x^{\frac{5}{2}}) = \frac{15 x ^{\frac{3}{2}}}{2}

\frac{d}{d x} (2) = 0

= 16 x^{3} - \frac{15 x ^{\frac{3}{2}}}{2} + 0

Vereinfache

= 16 x^{3} - \frac{15 x ^{\frac{3}{2}}}{2}

\frac{\partial}{\partial x} (3 e^{y} + x + x^{3} + 6)

y^{^{'}} = 2 x y^{2}

f (x) = 7 e^{x}

\frac{d}{d x} (\frac{4 b}{a} x a^{2} - x^{2})

j o in 1 - 4 x + f (x)