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Beliebt Rechnen >

derivative of (x+4^3(x-3)^6)

Lösung

\frac{d}{d x} ((x + 4)^{3} (x - 3)^{6})

Lösung

3 (x + 4)^{2} (x - 3)^{6} + 6 (x - 3)^{5} (x + 4)^{3}

Schritte zur Lösung

\frac{d}{d x} ((x + 4)^{3} (x - 3)^{6})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = (x + 4)^{3}, g = (x - 3)^{6}

= \frac{d}{d x} ((x + 4)^{3}) (x - 3)^{6} + \frac{d}{d x} ((x - 3)^{6}) (x + 4)^{3}

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

\frac{d}{d x} ((x - 3)^{6}) = 6 (x - 3)^{5}

= 3 (x + 4)^{2} (x - 3)^{6} + 6 (x - 3)^{5} (x + 4)^{3}

Graph

Beliebte Beispiele

limit as x approaches 4 of 2-sqrt(x)

x \to 4 lim (2 - x)

tangent y=3x-7sqrt(x)

t an g e n t y = 3 x - 7 x

derivative sqrt(x+4y)+sqrt(2xy)

d er i v a t i v e x + 4 y + 2 x y

integral of 4x+10

\int 4 x + 10 d x

y^'-4y=-3e^{3t},y(0)=9

y^{^{'}} - 4 y = - 3 e^{3 t}, y (0) = 9