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Beliebt Rechnen >

derivative of 1/3 (16+x^2^{3/2}+16/3)

Lösung

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3})

Lösung

x (x^{2} + 16)^{\frac{1}{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}} + \frac{16}{3})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}}) + \frac{d}{d x} (\frac{16}{3})

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{\frac{3}{2}}) = x (16 + x^{2})^{\frac{1}{2}}

\frac{d}{d x} (\frac{16}{3}) = 0

= x (16 + x^{2})^{\frac{1}{2}} + 0

Vereinfache

= x (x^{2} + 16)^{\frac{1}{2}}

Graph

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