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Beliebt Rechnen >

derivative f(x)=1.5x^7-(x^4)/3+pix-ex^2+sqrt(2)

Lösung

ableitung von

f (x) = 1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2

Lösung

10.5 x^{6} - 1.33333 \dots x^{3} - 5.43656 \dots x + π

Schritte zur Lösung

\frac{d}{d x} (1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2)

Vereinfache

1.5 x^{7} - \frac{x ^{4}}{3} + π x - e x^{2} + 2 : 1.5 x^{7} - 0.33333 \dots x^{4} + π x - e x^{2} + 1.41421 \dots

= \frac{d}{d x} (1.5 x^{7} - 0.33333 \dots x^{4} + π x - e x^{2} + 1.41421 \dots)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (1.5 x^{7}) - \frac{d}{d x} (0.33333 \dots x^{4}) + \frac{d}{d x} (π x) - \frac{d}{d x} (e x^{2}) + \frac{d}{d x} (1.41421 \dots)

\frac{d}{d x} (1.5 x^{7}) = 10.5 x^{6}

\frac{d}{d x} (0.33333 \dots x^{4}) = 1.33333 \dots x^{3}

\frac{d}{d x} (π x) = π

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

\frac{d}{d x} (1.41421 \dots) = 0

= 10.5 x^{6} - 1.33333 \dots x^{3} + π - 2 e x + 0

Vereinfache

= 10.5 x^{6} - 1.33333 \dots x^{3} - 5.43656 \dots x + π

Graph

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