derivative f(x)=4x^{5/4}+8x^{3/2}+2x

Lösung

ableitung von

f (x) = 4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 2 x

5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 2

Schritte zur Lösung

\frac{d}{d x} (4 x^{\frac{5}{4}} + 8 x^{\frac{3}{2}} + 2 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} (8 x^{\frac{3}{2}}) + \frac{d}{d x} (2 x)

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

\frac{d}{d x} (8 x^{\frac{3}{2}}) = 12 x^{\frac{1}{2}}

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

= 5 x^{\frac{1}{4}} + 12 x^{\frac{1}{2}} + 2

t an g e n t f (x) = \frac{2}{x}, at \frac{1}{16}

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

\int (x^{5} - 10 x^{4} + x^{3} - 15 x^{2}) d x

n = 1 \sum \infty \frac{z ^{n}}{n ^{2}}

\frac{d y}{d x} = x + 3