derivative f(x)=4x^{5/4}+10x^{3/2}+3x

Lösung

ableitung von

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

5 x^{\frac{1}{4}} + 15 x^{\frac{1}{2}} + 3

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (4 x^{\frac{5}{4}}) = 5 x^{\frac{1}{4}}

\frac{d}{d x} (10 x^{\frac{3}{2}}) = 15 x^{\frac{1}{2}}

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

= 5 x^{\frac{1}{4}} + 15 x^{\frac{1}{2}} + 3

\int x^{5} x^{6} - 1 d x

a re a x^{2} + 4 x + 3, y = - 1, x = 0, [- 2, 0]

k = 1 \sum \infty (20)^{k}

\int_{- 4}^{4} ∣ x - 3 ∣ d x

d er i v a t i v e f (x) = (\frac{x ^{3}}{x ^{8} + 5})^{2}