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Beliebt Rechnen >

derivative of-3/2 sqrt(x^3)-2x^5-5x^2

Lösung

\frac{d}{d x} (- \frac{3}{2} x^{3} - 2 x^{5} - 5 x^{2})

Lösung

- \frac{9 x}{4} - 10 x^{4} - 10 x

Schritte zur Lösung

\frac{d}{d x} (- \frac{3}{2} x^{3} - 2 x^{5} - 5 x^{2})

Vereinfache

- \frac{3}{2} x^{3} - 2 x^{5} - 5 x^{2} : - \frac{3 x ^{3}}{2} - 2 x^{5} - 5 x^{2}

= \frac{d}{d x} (- \frac{3 x ^{3}}{2} - 2 x^{5} - 5 x^{2})

Wende die Summen-/Differenzregel an:

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

= - \frac{d}{d x} (\frac{3 x ^{3}}{2}) - \frac{d}{d x} (2 x^{5}) - \frac{d}{d x} (5 x^{2})

\frac{d}{d x} (\frac{3 x ^{3}}{2}) = \frac{9 x}{4}

\frac{d}{d x} (2 x^{5}) = 10 x^{4}

\frac{d}{d x} (5 x^{2}) = 10 x

= - \frac{9 x}{4} - 10 x^{4} - 10 x

Graph

Beliebte Beispiele

derivative of 1+3sqrt(x)

\frac{d}{d x} (1 + 3 x)

(dy)/(dx)= 1/(4y^3)

\frac{d y}{d x} = \frac{1}{4 y ^{3}}

derivative of (x^2-49/(x-7))

\frac{d}{d x} (\frac{x ^{2} - 49}{x - 7})

integral of sqrt(2+2sin(θ))

\int 2 + 2 sin (θ) d θ

(dy)/(dx)=2x+3y-1

\frac{d y}{d x} = 2 x + 3 y - 1