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Beliebt Rechnen >

derivative f(x)=7+2x+x^3(5x^2+1)^5

Lösung

ableitung von

f (x) = 7 + 2 x + x^{3} (5 x^{2} + 1)^{5}

Lösung

50 x^{4} (5 x^{2} + 1)^{4} + 3 x^{2} (5 x^{2} + 1)^{5} + 2

Schritte zur Lösung

\frac{d}{d x} (7 + 2 x + x^{3} (5 x^{2} + 1)^{5})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (7) + \frac{d}{d x} (2 x) + \frac{d}{d x} (x^{3} (5 x^{2} + 1)^{5})

\frac{d}{d x} (7) = 0

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

\frac{d}{d x} (x^{3} (5 x^{2} + 1)^{5}) = 3 x^{2} (5 x^{2} + 1)^{5} + 50 x^{4} (5 x^{2} + 1)^{4}

= 0 + 2 + 3 x^{2} (5 x^{2} + 1)^{5} + 50 x^{4} (5 x^{2} + 1)^{4}

Vereinfache

= 50 x^{4} (5 x^{2} + 1)^{4} + 3 x^{2} (5 x^{2} + 1)^{5} + 2

Graph

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