derivative of 4x^{5/4}+6x^{3/2}+9x

Lösung

\frac{d}{d x} (4 x^{\frac{5}{4}} + 6 x^{\frac{3}{2}} + 9 x)

5 x^{\frac{1}{4}} + 9 x^{\frac{1}{2}} + 9

Schritte zur Lösung

\frac{d}{d x} (4 x^{\frac{5}{4}} + 6 x^{\frac{3}{2}} + 9 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} (6 x^{\frac{3}{2}}) + \frac{d}{d x} (9 x)

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

\frac{d}{d x} (6 x^{\frac{3}{2}}) = 9 x^{\frac{1}{2}}

\frac{d}{d x} (9 x) = 9

= 5 x^{\frac{1}{4}} + 9 x^{\frac{1}{2}} + 9

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